Given sin theta = -3/5 and 0 is in quad 2, find Cos theta and tan theta
Sorry, QII angles have positive sin > 0
To find the values of cos(theta) and tan(theta) given sin(theta) = -3/5 and quadrant 2, you can use the Pythagorean identity and the unit circle.
Let's start by finding the value of cos(theta). The Pythagorean identity states that sin^2(theta) + cos^2(theta) = 1. Since we know that sin(theta) = -3/5, we can substitute this value into the equation:
(-3/5)^2 + cos^2(theta) = 1
9/25 + cos^2(theta) = 1
cos^2(theta) = 1 - 9/25
cos^2(theta) = 16/25
Since cosine is positive in quadrant 2, we can take the positive square root:
cos(theta) = √(16/25)
cos(theta) = 4/5
Next, let's find the value of tan(theta). Tan(theta) is the ratio of sin(theta) to cos(theta). We already know the values of sin(theta) and cos(theta):
tan(theta) = sin(theta) / cos(theta)
tan(theta) = (-3/5) / (4/5)
tan(theta) = -3/4
Therefore, cos(theta) = 4/5 and tan(theta) = -3/4.