Given cosθ=−4√20, where 0∘≤θ≤180∘ ?

1 Answer
Douglas K.
Jun 20, 2018

θ≈153.4∘

Explanation:

Given cos(θ)=−4√20,0∘≤θ≤180∘

Use the inverse cosine on both sides:

θ=cos−1(−4√20),0∘≤θ≤180∘

θ≈153.4∘

You have the value for the cosine function the denominator should be rationalized:

cos(θ)=−4√20

cos(θ)=−42√5

cos(θ)=−2√55

The secant function is the reciprocal of the cosine function:

sec(θ)=1cos(θ)

sec(θ)=−√52

The sine function can be found using the identity:

sin(θ)=±√1−cos2(θ)

sin(θ)=± ⎷1−(−2√55)2

sin(θ)=±√2525−2025

sin(θ)=±√55

We know that the sine function is positive in the second quadrant:

sin(θ)=√55

The cosecant function is the reciprocal of the sine function:

csc(θ)=1sin(θ)

csc(θ)=5√5

csc(θ)=√5

Find the tangent function using the identity:

tan(θ)=sin(θ)cos(θ)

tan(θ)=√55−2√55

tan(θ)=−12

The cotangent function is the reciprocal of the tangent function:

cot(θ)=−2

Related questions
Impact of this question
1426 views around the world
You can reuse this answer
Creative Commons License