Evaluating the Six Trigonometric Functions

Angle θ is in standard position. if sin(θ) = −1/3 and π < θ < 3π2 , find cos(θ).

-2√2 / 3

The point (-7, -24) is on the terminal ray of angle θ which is in standard position. A student found the six trigonometric values for angle θ. The student's answers are shown. Which value(s) are incorrect?

a : sin c : tan d : csc f : cot

Angle A is in standard position and terminates in quadrant IV. If sec(A)=4/3, complete the steps to find cot(A). Use to identify _________to find the value of___________(a) Solving the identity, tan(A) = _____. What is cot(A)?

first blank) tan²(A) + 1 = sec²(A) ✔ the second blank) tan third blank) positive √7/3 What is cot(A)? negative 3√7 / 7

Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.

sin(θ) = -15/17 ✔ cos(θ) = 8/17 ✔ tan(θ) = -15/8 ✔ csc(θ) = -17/15 ✔ sec(θ) = 17/8 ✔ cot(θ) = -8/15 ✔

cosθ=-√2/2,and 3π/2<θ< 2π, evaluate sin(θ) and tan(θ)

sin(θ)= negative √2/2 tan(θ)= negative 1

The point (5, −2) is on the terminal ray of angle θ, which is in standard position. Without evaluating, explain how you would find the values of the six trigonometric functions.

Plot the point (5, -2) and draw a line from the point to the x-axis to make a right triangle. Use the Pythagorean theorem to find the length of the hypotenuse. Use the definition of each trigonometric function to find the values. Determine the appropriate sign for each function, using the fact that the terminal side is in Quadrant IV.