The angle theta is in the fourth quadrant and costheta=frac{2}{7}. Find the exact value of the remaining five trigonometric functions.

Suman Cole

Suman Cole

Answered question

2021-02-09

The angle θ is in the fourth quadrant and cosθ=27. Find the exact value of the remaining five trigonometric functions.

Answer & Explanation

hajavaF

hajavaF

Skilled2021-02-10Added 90 answers

It is given that θ is in the fourth quadrant and
cos(θ)=27
Since,
cos(θ)=Base(B)Hypotenuse(H)cosθ and secθ
BH=27
Then,
B=2,H=7
Use Pythagoras formula to find the perpindicular P,
H2=B2+P2
P2=H2B2
=7222
=494
=45
That is,
P=45
All the trigonometric ratios except cosθ and secθ are negative as θ is in the fourth quadrant. Then
secθ=1cosθ
=127
=72
And sinθ=PH=457
cscθ=HP=745
tanθ=PB=452
cotθ=BP=245
Hence, the required value of the remaining trigonometric ratios is
secθ=72,sinθ=457,cscθ=745,tanθ=452,cotθ=245

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