Problem

Find the exact value of each of the remaining trigonometric functions of θ. Rationalize denominators when applicable. sin⁡θ=35 given that θ is in quadrant I

Answer

Expert–verified
Hide Steps
Answer

Final Answer: The exact values of the remaining trigonometric functions of θ are cos⁡θ=45,tan⁡θ=34,csc⁡θ=533,sec⁡θ=54, and cot⁡θ=433

Steps

Step 1 ：We are given that sin⁡θ=35 and θ is in quadrant I.

Step 2 ：We can use the Pythagorean identity sin2⁡θ+cos2⁡θ=1 to find the value of cos⁡θ.

Step 3 ：Since θ is in quadrant I, cos⁡θ will be positive.

Step 4 ：Solving for cos⁡θ we get cos⁡θ=45.

Step 5 ：We can then find the other trigonometric functions using the definitions of those functions in terms of sin⁡θ and cos⁡θ.

Step 6 ：We find that tan⁡θ=34, csc⁡θ=533, sec⁡θ=54, and cot⁡θ=433.

Step 7 ：Final Answer: The exact values of the remaining trigonometric functions of θ are cos⁡θ=45,tan⁡θ=34,csc⁡θ=533,sec⁡θ=54, and cot⁡θ=433

link_gpt

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find y′ if $y=\ln \… 3. (3pts) Cherry trees in a c… More