Evaluating the Six Trigonometric Functions — Unit test Answers

A student is given that point P(a, b) lies on the terminal ray of angle , which is between radians and 2 radians. The student uses the steps below to find cos . Step 1Find the quadrant in which P(a, b) lies:P(a, b) is in Quadrant IV.Step 2Use the point and the Pythagorean theorem to determine the value of r:, but since r must be positive, .Step 3Determine cos ., where a and b are positive.Which of the following explains whether the student is correct?

The lengths of two sides of a right triangle are 12 inches and 15 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.

A student uses the equation to represent the speed, s, in feet per second, of a toy car driving around a circular track having an angle of incline , where . To solve the problem, the student used the given value of to find the value of and then substituted the value of in the equation above to solve for s. What is the approximate value of s, the speed of the car in feet per second?

For which value of is cot () undefined?

The longest side of an isosceles obtuse triangle measures 20 centimeters. The other two side lengths are congruent but unknown.What is the greatest possible whole-number value of the congruent side lengths?

Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a 25o angle with the ground and when the string makes a 45o angle with the ground? Round to the nearest tenth.

Triangles A B C and X Y Z are shown. Angles A B C and X Y Z are right angles. Angles B A C and Y X Z are congruent. The length of A B is 5, the length of A C is 13, and the length of B C is 12.

An angle in standard position measures radians, and P(0, 1) is on the terminal side of the angle. What is the value of the cosine of this angle?

Which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle?

If a vertical line is dropped from the x-axis to the point (12, –9) in the diagram below, what is the value of sec ?

What are the exact values of the six trigonometric functions for radians?

Jamel is asked to create triangles using three of four given sticks. The sticks measure 3 in., 6 in., 7 in., and 8 in. He creates these 4 triangles.Triangle 1: 3 in., 6 in., 7 in.Triangle 2: 3 in., 6 in., 8 in.Triangle 3: 3 in., 7 in., 8 in.Triangle 4: 6 in., 7 in., 8 in.