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
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