Sin & Cos Equation/Relation

Question

If sin(x) = 0.3, find cos(pi-x)

how i would solve this:

• let x = sin-1(0.3)
• solve for cos(pi-[sin-1(0.3)])

Is there a way to solve this by hand?

Is the above method wrong?

Answer 1

If $\sin x=0.3$, $$\cos(\pi-x)=-\cos(x)=\pm\sqrt{1-\sin^2(x)}=\pm\frac{\sqrt{91}}{10}$$

Answer 2

$$cos(\pi-x)=sin\pi sin x+cos\pi cos x=0+cos\pi cos x=-cos x= -\sqrt{1-sin^2 x}\; (0\leq x\leq \pi/2)$$