precalculus

10 questions

1. Match the right triangle definition with its trigonometric function.

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(a)      Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper	hyp adj						=
(b)	opp adj
(c)	opp hyp
(d)	adj opp
(e)	hyp opp
(f)	adj hyp

2. Use the figure to answer the question.
What is the length of the side opposite the angle θ?

3. Use the figure to answer the question.
What is the length of the hypotenuse?

4. Find the exact values of the six trigonometric functions of the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle. Let b = 5 and c = 13.)

sin(θ)

=

cos(θ)

=

tan(θ)

=

csc(θ)

=

sec(θ)

=

cot(θ)

=

5. Find the exact values of the six trigonometric functions of the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)

sin θ

=

cos θ

=

tan θ

=

csc θ

=

sec θ

=

cot θ

=

6. Find the exact values of the six trigonometric functions of the angle θ for the triangle.

sin θ

=

cos θ

=

tan θ

=

csc θ

=

sec θ

=

cot θ

=

7. Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of θ.

sin(θ) = 12/37

cos(θ)

=

tan(θ)

=

csc(θ)

=

sec(θ)

=

cot(θ)

=

8. Construct an appropriate triangle to complete the table. (0 ≤ θ ≤ 90°, 0 ≤ θ ≤ π/2)

     Function     

     θ (deg)     

     θ (rad)     

     Function Value     

cos

150°

9. Construct an appropriate triangle to complete the table. (0 ≤ θ ≤ 90°, 0 ≤ θ ≤ π/2)

     Function     

     θ (deg)     

     θ (rad)     

     Function Value     

sec

°

π

4

10. Use a calculator to evaluate each function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.)

(a) tan(20°)

(b) cot(70°)