SOLUTION: Let alpha be the arc such that: alpha belongs to ] pie over 2, pie[ and cos alpha= -12 over 13. Without using a calculator find sin alpha and tan alpha

Question 1198891: Let alpha be the arc such that: alpha belongs to ] pie over 2, pie[ and cos alpha= -12 over 13. Without using a calculator find sin alpha and tan alpha
Found 2 solutions by Alan3354, math_tutor2020:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Let alpha be the arc such that: alpha belongs to ] pie over 2, pie[ and cos alpha= -12 over 13. Without using a calculator find sin alpha and tan alpha
==========================
Pie is a round dessert.
Use the Greek letter pi unless it's a pie chart.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Angle alpha is on the interval ]pi/2, pi[ which is equivalent to saying pi/2 < alpha < pi
Each endpoint is excluded.

Because pi/2 < alpha < pi, this angle is in quadrant Q2, which is in the northwest corner.

In Q2 we have these facts:
cosine is negative
sine is positive
tangent is negative

cos(alpha) = -12/13 = adjacent/hypotenuse
adjacent = -12
hypotenuse = 13

Use the pythagorean theorem to find the opposite side is 5 units long.

opposite = 5
adjacent = -12
hypotenuse = 13

Then,
sin(alpha) = opposite/hypotenuse
sin(alpha) = 5/13
and
tan(alpha) = opposite/adjacent
tan(alpha) = 5/(-12)
tan(alpha) = -5/12

Diagram:

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