Cos D= -3/4. if the sine of the angle is positive, find the sine of the angle and determine the quadrant.
Can anyone tell me the steps. I need to learn this.
sin^2 D = 1 - cos^2 D
The sin is + and the cos is - in Quadrant 2
Is cos^2D= 9/16
yes, cosine squared of D is 9/16
Soo what is the squareroot of 7/16?
1/4 sqrt7
To find the sine of the angle and determine the quadrant, we first need to use the Pythagorean Identity to find the value of the cosine:
cos^2θ + sin^2θ = 1
Since cosθ = -3/4, we can substitute it into the identity:
(-3/4)^2 + sin^2θ = 1
Simplifying:
9/16 + sin^2θ = 1
sin^2θ = 1 - 9/16
sin^2θ = 7/16
Taking the square root of both sides:
sinθ = ±√(7/16)
Now, since we know that the sine of the angle is positive, we can take the positive square root:
sinθ = √(7/16)
To determine the quadrant, we need to consider the signs of both sine and cosine in different quadrants.
In the first quadrant (0° to 90°), both the sine and cosine are positive.
In the second quadrant (90° to 180°), the sine is positive while the cosine is negative.
In the third quadrant (180° to 270°), both the sine and cosine are negative.
In the fourth quadrant (270° to 360°), the sine is negative while the cosine is positive.
Since the sine of the angle is positive, we can conclude that the angle is in either the first or the second quadrant.