The angle θ lies in Quadrant II .
sinθ=34
What is cosθ ?
−7√/4
7√/4
3/4
−3/4 <my answer
Assuming you meant
sinθ=3/4
The hypotenuse is 4, so the other leg is √(16-9) = √7
In QII, x<0. Since cosθ = x/r
cosθ = -√7/4
You should immediately have known your answer was wrong, because
sin^2θ + cos^2θ = 1
To find cosθ, we can use the Pythagorean identity for trigonometric functions: sin^2θ + cos^2θ = 1. Since we are given that sinθ = 34, we can start by substituting this value:
(34)^2 + cos^2θ = 1
1156 + cos^2θ = 1
Next, isolate cos^2θ by subtracting 1156 from both sides:
cos^2θ = 1 - 1156
cos^2θ = -1155
At this point, we may realize that there is a mistake in the given information. The value of sinθ can never exceed 1 or be negative, so sinθ cannot be 34.
However, if we assume that sinθ = 3/4 instead, we can recalculate:
(3/4)^2 + cos^2θ = 1
9/16 + cos^2θ = 1
Now, isolate cos^2θ:
cos^2θ = 1 - 9/16
cos^2θ = 7/16
Taking the square root of both sides, we find:
cosθ = ±√(7/16)
Since the angle θ lies in the second quadrant, cosθ must be negative. Thus, the correct answer is:
cosθ = -√(7/16) = -7√/4
Therefore, the correct answer is −7√/4.