TRIGONOMETRY PROBLEMS
Whether needing help with homework or reviewing for tests, Mr. X helps students better understand Trigonometry. Our sample trig problems provide the practice needed to grasp all angles of Trigonometry. The trig problems reinforce our library of trigonometry math lessons. Check out our free samples below, as well as the trigonometry problem set.
Trigonometry Sample Problems 1
Trigonometry Sample Problems 2
Trigonometry Sample Problems
General Topics
General Topics 


Title/Subject  Description  
Find Trig Values at 660° Version E  Find the values of the six basic trigonometric functions at 660°. This is Version E (the explanatory) version. 

Find Trig Values at 660° Version F  Find the values of the six basic trigonometric functions at 660°. This is Version F, the "fast" version. 

Find Trig Values at 660° Version G  Find the values of the six basic trigonometric functions at 660°. This is Version G, the general version. 

Inverse Trigonometric Ratios 14016  Inverse trig functions RETURN THE ANGLE whose trig function is that number.  
Inverse Trigonometric Ratios 14018  Inverse trigonometric functions return the angle whose trig function is that number.  
Old Fashioned Problems 04  The nature of trigonometry lends itself to tables and identities, which were far more important in days gone by than today with our calculating machines. Nevertheless, it's good to understand these relationships. 

Solve 2 cos 3x + 1 = 0 Version E  Given the equation 2 cos 3x + 1 = 0, we solve for the value of x that makes the statement true. This is Version E, the explanatory version. 

Solve 2 cos 3x + 1 = 0 Version F  Given the equation 2 cos 3x + 1 = 0, we solve for the value of x that makes the statement true. This is Version F, the fast and fun version. 

Solve 2 cos 3x + 1 = 0 Version G  Given the equation 2 cos 3x + 1 = 0, we solve for the value of x that makes the statement true. This is Version G, the general version. 

Solving right Triangles  From MathAids.com, a worksheet to determine the length of a side of a right triangle given two sides and one angle.  
Solving Triangles 01  Six problems to solve triangles using the Law of Cosines and the Law of Sines.  
Trig Equations 03  Trigonometric equations in x, where x represents an angle specified to reside within a range of values. We solve for x. 

Trig Problem 11  Pythagorean Triples  Basic right triangles are solved with integer values for the lengths of the sides. We call these Pythagorean Triples. No irrational numbers are required. 

Trig Problem 12  Pythagorean relations with irrational lengths  We solve right triangles with various lengths of the sides. The Pythagorean relation holds, where the sum of the squares of the legs (the perpendicular sides) is equal to the square of the hypotenuse (the square of the longest side). 

Trig Problem 13  Pythagorean relations with sines and cosines  We solve for the sine and cosine of an acute angle within a right triangle.  
Trig Problem 14  Sines and cosines of acute angles in right triangles  We practice with irrational numbers as we find the sine and cosine of acute angles within right triangles.  
Trig Problem 15  Exact values of sines and cosines for important angles  We practice the sine values and the cosine values for multiples of 30 degrees and 45 degrees.  
Trig Problem 16  Reference angles  We like to say that reference angles are "the fastest way back to the xaxis." The acute angle between the terminal ray of an angle that is in standard position and the xaxis is termed the Reference Angle, or Related Angle.  
Trig Problem 17  Reference Angles given  Provided reference angles and the Quadrant bearing the terminal side of the angle in standard position, sketch the appropriate angle.  
Trig Problem 18  Important angles in degrees and radians  It is important to know the values of important angles around the unit circle, namely, the multiples of 30 degrees and 45 degrees. In radians, these are multiples of pi/6 and pi/4, respectively. 

Trig Problem 19  The classic ladderagainstthewall  Every trig course includes at least one problem of a ladder of fixed length resting against a vertical wall.  
Trig Problem 20  Real cities in a right triangle: Evanston, Ames, and Sheboygan  We look at the relationship between cities in the Midwest (Midwestern United States) that form a right triangle. Conveniently, we ignore the curvature of the earth. The focus of this problem is bearing, or compass heading. 

Trig Problem 21  Pottstown and Trenton, a helicopter and a rate  This is a distanceratetime problem. As distance is the product of rate (speed) and time, we use trig to calculate when a helicopter on a particular bearing, traveling at a specified speed, will be closest to Pottstown. 

Trig Problem 22  Given a chord length and a central angle, find radius  When provided a chord length as well as the central angle formed by the endpoints of the chord with the center of the circle, we may determine the radius of the circle.  
Trig Problem 23  Circumference versus perimeter of 60sided regular polygon  In this problem we compare the circumference of a circle to the perimeter of a regular 60sided polygon inscribed within it.  
Trig Problem 24  Angles from a lighthouse to tides high and low  We examine two right triangles to determine the relation between the angle of depression from the top of a lighthouse to both high tide and low tide.  
Trig Problem 25  Mountain peak angle  As we get closer to the base of the mountain, the angle of elevation to the peak increases. From two points in the plane of the base of the mountain, and the angles of elevation, we calculate the height of the mountain above the plane (plain). 

Trig Problem 26  Classic ladder before and after moving the base  Just as we always have a static ladder problem in every trig course, we always have a problem where the base of the ladder is moved in a second scenario. How far does the top of the ladder rise when we move the ladder's base a fixed distance toward the wall? 

Trig Problem 26B  Another approach to Problem 26  In this solution to Problem 26 we use a Pythagorean relation instead of a trig function to derive the answer.  
Trig Problem 27  Multifunctional statements to single functions  Here we take expressions with multiple functions within them and express each in terms of a single trig function.  
Trig Problem 28  Simplify some trig  Many trig functions can be simplified, similar to what we do in algebra. In fact, much of this kind of work in trig class can be categorized as algebra. 

Trig Problem 29  Change the terms  Trig functions have the interesting property of being able to be expressed in terms other trig functions. Consequently, the numbers associated with trig functions of angles can be expressed in terms of other trig functions. 

Trig Problem 30  The shadow knows  As the earth turns the sun appears to move through the sky. We calculate the time at which a specified length of shadow appeared from a tower of known height. 

Trig Problem 31  Angles in degrees and radians  We reinforce the knowledge of important values of angles as we traverse the unit circle.  
Trig Problem 32  Identify angles as multiples of 45 degrees  We reinforce the angles that are multiples of 45 degrees, or pi/4 radians.  
Trig Problem 33  Differences between basic angles  In both degrees and radians, it is good to see the differences between important angles.  
Trig Problem 34  Coordinates on unit circle for important angles  It is imperative to know the x and y values for the points on the unit circle that lie on important angles, such as multiples of 30 degrees and multiples of 45 degrees. As we label points (x, y) we label cosine Θ and sine Θ, respectively. 

Trig Problem 35  More important angle values  We examine six important angles in Quadrants II, III, and IV, with reference angles of 30 degrees and 60 degrees, or π/6 and π/3, respectively.  
Trig Problem 36  Round to four decimal places  This problem simply asks to express values from trig functions of specified angles to four decimal places, or to the nearest ten thousandth.  
Trig Problem 37  Sine of the times  You are asked to express various functions in terms of sine. The sine function is the only one "allowed" for expressing the other five basic trig functions. 

Trig Problem 38  Prove the identity  Prove the identity. An identity is an expression that is always true. In other words, show that one side of the equality will always be equal to the other side of the equality. 

Trig Problem 39  Prove the identity  Prove the identity. An identity is an expression that is always true. In other words, show that one side of the equality will always be equal to the other side of the equality. Here we ask that you prove: sin Θ cot Θ sec Θ = 1. 

Trig Problem 40  Prove the identity  Prove the identity. An identity is an expression that is always true. In other words, show that one side of the equality will always be equal to the other side of the equality. This proof invovles the functions of sinΘ, cos Θ, and tan Θ. 

Trig Problem 41  Prove the identity  Prove the identity. An identity is an expression that is always true. In other words, show that one side of the equality will always be equal to the other side of the equality. You are to show that sin²α + tan²ß + cos²α = sec²ß. 

Trig Problem 42  Prove the identity  Prove the identity. An identity is an expression that is always true. In other words, show that one side of the equality will always be equal to the other side of the equality. This proof involves both cotangents and cosecants. 

Trig Problem 43  Prove the identity  Prove the identity. An identity is an expression that is always true. In other words, show that one side of the equality will always be equal to the other side of the equality. Both secant and cosine appear, but it's more than just a reciprocal relationship. the proof has a couple of ones, a fraction, and two negatives. 

Trig Problem Set 01  Given a basic trig function value for some angle, determine the other basic trig function values for that angle.  
Trig Problem Set 02  Basic calculations of trig function values; these are the earliest problems in plane trig.  
Trig Problem Set 03  Given a value for a basic trig function on an angle, find the values for the other five basic trig functions on that angle.  
Trig Values 02  Given a trig value and an associated angle, determine the values of the other five basic trig function values for that angle.  
Trigonometric Ratios 14015  Eight problems on a worksheet from MathAids.com, we solve for the trig value for one angle in a right triangle. 