Find the exact value of each of the remaining trigonometric function of theta.displaystyle

Dolly Robinson

Dolly Robinson

Answered question

2021-01-31

Find the exact value of each of the remaining trigonometric function of θ.
cosθ=2425,270<θ<360
sinθ=?
tanθ=?
secθ=?
cscθ=?
cotθ=?

Answer & Explanation

Ayesha Gomez

Ayesha Gomez

Skilled2021-02-01Added 104 answers

Step 1
Given:
cosθ=2425,270<θ<360
So the angle lies in fourth quadrant. In the fourth quadrant cosine and secant are positive all others are negative.
Pythagorean identity is used for finding sine value
sin2θ+cos2θ=1
sinθ=±1cos2θ
=±1(2425)2
=±252242252
=725
The sine value is negative since angle is in third quadrant.
Step 2
The tan value can be found as
tanθ=sinθcosθ
=7252425
=724
Step 3
Secant is reciprocal of cosine.
secθ=1cosθ
=12425
=2524
Step 4
Cosecant is the reciprocal of sine.
cscθ=1sinθ
=1725
=257
Step 5
Cot is the reciprocal of tan
cotθ=1tanθ
=1724
=247

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