Question

Simplifying steps without using the calculator for:
tan(cos^-1(-1/10))
cos(sin^−1(1/x)) Assume x is positive
tan(cos^−1(12/13))
cos^−1(cos 150°)



This is pretty much the entire section we are doing. My teacher is a robot and has us self teach ourselves. Can someone please tell me how I am supposed to do these without a calculator???

Answer 1

last one: the angle whose cosine is cosine of 150? You have to be kidding..150.

next to last one:
tan theta=sinTheta/cosTheta where theta is arccos12/13
hmmm then you have
sin arcsos( )/cos arc cos( ) or
sin arecos ( ). Now draw the triangle, isn't it a a 5 12 13 triangle. so the sin is 5/13? check that.

the second one. draw the triangle. I see the last side as sqrt (x^2 -1). so cos must be sqrt(1-x^2)/x

So, how are you supposed to do these without a calculator? Analyze the expressions.