Question

Cos(0)=-7/8 if 0 is an angle in quandrant II what is the value of tan(0)

Answer 1

To find the value of tan(0) for an angle in quadrant II where cos(0) = -7/8, we calculate sin(0) using the Pythagorean identity, which is positive in quadrant II, and then divide sin(0) by cos(0) to get tan(0). The final value of tan(0) is -√15/7.

Step-by-step explanation:

If cos(0) = -7/8 and 0 is an angle in quadrant II, we know that the cosine of an angle in quadrant II is negative, and since the cosine represents the x-coordinate on the unit circle, this tells us that we're on the left side of the unit circle (x is negative). In quadrant II, the sine of an angle is positive because the y-coordinate is positive.

To find tan(0), we use the identity tan(0) = sin(0)/cos(0). Since we only have cos(0), we need to find sin(0). We can do this using the Pythagorean identity sin2(0) + cos2(0) = 1. Then, sin(0) will be positive because we are in quadrant II. Let's calculate this step-by-step:

1. cos2(0) = (7/8)2 = 49/64.
2. sin2(0) = 1 - cos2(0) = 1 - 49/64 = 15/64.
3. sin(0) = √(15/64), and since we're in quadrant II, sin(0) is positive, so sin(0) = √(15)/8.
4. Finally, tan(0) = sin(0)/cos(0) = (√(15)/8) / (-7/8) = -√(15)/7.

The value of tan(0) when cos(0) = -7/8 and the angle 0 is in the second quadrant is -√(15)/7.