SOLUTION: 1. If cos Θ = negative two over five and tan Θ > 0, what is the value of sin Θ? 2. Engineers are analyzing the performance of windshield wiper blades. At the end

Algebra ->  Trigonometry-basics -> SOLUTION: 1. If cos Θ = negative two over five and tan Θ > 0, what is the value of sin Θ? 2. Engineers are analyzing the performance of windshield wiper blades. At the end      Log On


   

Question 881667: 1. If cos Θ = negative two over five and tan Θ > 0, what is the value of sin Θ?
2. Engineers are analyzing the performance of windshield wiper blades. At the end of one swipe, the tip of a blade is at (−5, 7) when represented graphically. What is the sine value of this function?
3. For an angle Θ with the point (5, −12) on its terminating side, what is the value of cosine?

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
1. Quadrant 3.
cos%28theta%29=-2%2F5, but if tangent is positive, the angle must be quadrant 3. This means also that sin%28theta%29%3C0.
Letting y=sine,
%28-2%2F5%29%5E2%2By%5E2=1
y%5E2=1-4%2F25
y=-sqrt%28%2825-4%29%2F25%29
highlight%28y=-sqrt%2821%29%2F5%29

3. Quadrant 4. Cosine is positive.
Radius is sqrt%2825%2B144%29=sqrt%28169%29=13.
highlight%28cos%28theta%29=5%2F13%29