SAT Math Problem (20)

Question

If x represents the radian measure of an angle, where 0 <  x <  π/2, and sin x = 5/13, then what is the value of tan(π/2 -x)?

 

Note: I got so far as realizing that it is a 5,12,13 right triangle, but I don't think I am familiar enough with radians to solve this problem. So if you could briefly explain radians and how to maneuver them, that would be very invaluable to me!

Answer 1

The mentioning of radians is a red herring (SAT does that a lot!).

tan (π/2 - θ) = cot θ

cot θ = cos θ / sin θ

cos θ / sin θ = 12/5

 

tan (π/2 - θ) = 12/5

Answer 2

Just convert radians into degrees!  pi/2 = 90^o.

 

In general pi radians = 180^o; dividing by 6 or 3 or 4 will give you the equivalent # of degrees.

 

radians are just another way of measuring angles. Analogously, you know about the different measures of temperature (Celsius and Fahrenheit). The conversion between degrees & radians is actually simpler than the conversion of temeratures!