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If the terminal side of angle θ goes through the point (10√10,310√10) on the unit circle, then what is cos(θ)?

Give an exact answer in the form of a fraction.

Sagot :

oladayoademosu

With terminal side of angle θ goes through the point (10√10,310√10) on the unit circle, then cosθ = 1/√962

Since the terminal side of the angle θ goes through the point (10√10,310√10) on the unit circle,

We have that tanθ = y/x where x = 10√10 and y = 310√10.

So, substituting the values of x and y into the equation, we have

tanθ = y/x

tanθ = 310√10/10√10

tanθ = 310/10

tanθ = 31

Using the trigonometric identity

1 + tan²θ = sec²θ

substituting tanθ = 31 into the equation, we have

1 + tan²θ = sec²θ

1 + 31² = sec²θ

1 + 961 = sec²θ

962 = sec²θ

sec²θ = 962

secθ = ±√962

Since secθ = 1/cosθ

1/cosθ = √962

cosθ = ±1/√962

Since both values of x and y are positive, we choose the positive answer since they are in the first quadrant.

So, cosθ = 1/√962

With terminal side of angle θ goes through the point (10√10,310√10) on the unit circle, then cosθ = 1/√962

Learn more about trigonometric functions here:

https://brainly.com/question/14121331

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