Answer:
tanΘ = -
Step-by-step explanation:
Using the trigonometric identities
• sin²x + cos²x = 1, hence
cosx = ± √(1 - sin²x )
• tanx =
given sinΘ = , then
cosΘ = ±
Since Θ is in the second quadrant where cosΘ < 0, then
cosΘ = -
= - = -
tanΘ =
= × -
= -
The exact measure of the angle is 45°.
<h3>How to get the angle?</h3>
We know that the terminal side passes through a point of the form (√2/2, y).
Notice that the point is on the unit circle, so its module must be equal to 1, so we can write:
We know that y is positive because the point is on the first quadrant.
Now, we know that our point is:
(√2/2, 1/√2)
And we can rewrite:
√2/2 = 1/√2
So the point is:
( 1/√2, 1/√2)
Finally, remember that a point (x, y), the angle that represents it is given by:
θ = Atan(y/x).
Then in this case, we have:
θ = Atan(1/√2/1/√2) = Atan(1) = 45°
If you want to learn more about angles, you can read: