Question

Coss=3/5​ and sint=−2/5​,s and t in quadrant IV

Use the cofunction identities to find an angle θ between 0∘ and 90∘ that makes the statement true.
cscθ=sec(2θ+75∘)
θ=___∘
(Type an integer or a simplified fraction.)

Answer 1

To find the angle θ that makes the statement true, you can use the cofunction identities for cosine and secant. By substituting the given values of sine and cosine into the cscθ = sec(2θ + 75°) identity and solving for θ, you can find the angle that satisfies the equation.

Step-by-step explanation:

To find the angle θ that makes the statement true, we can use the cofunction identities for cosine and secant:

Given that cosine is equal to 3/5 and sine is equal to -2/5 in quadrant IV, we can find the values of tangent, cosecant, and secant using the definitions of these trigonometric functions.

By substituting the values of sine and cosine into the identity cscθ = sec(2θ + 75°), we can solve for θ to find the angle that makes the statement true.

After substituting the values of sine and cosine and simplifying the equation, we find that θ is approximately 30°.