trignometry problem

[ladyazpy]

in the sketh, the size of angle theta is 335 degrees, the Y coordinate is -2

find the radius
find the value x coordinate
evaluate sin (squared) 335 + cos (squared) 335

 

[soroban]

Hello, ladyazpy!

in the sketch (?), the size of angle theta is 335 degrees, the Y coordinate is -2

(a) Find the radius.

(b) Find the x-coordinate.

(c) Evaluate \(\displaystyle \sin^2(335^o) \,+\,\cos^2(335^o)\)

I assume The Sketch looks like this:

          |
          |    x
      ----*------------
          | \ 25° :
          |   \   :y = -2
          |   r \ :
          |       * (x,-2)
          |

(a) We have: \(\displaystyle \,\sin25^o\,=\,\frac{2}{r}\;\;\Rightarrow\;\;r\,=\,\frac{2}{\sin25^o}\:\approx\:4.732\)

(b) We have: \(\displaystyle \,\tan25^o\,=\,\frac{2}{x}\;\;\Rightarrow\;\;x\,=\,2\cdot\tan25^o\:\approx\:0.933\)

(c) A rather silly question, isn't it?
\(\displaystyle \;\;\) For any angle \(\displaystyle \theta:\;\sin^2\theta\,+\,\cos^2\theta\:=\:1\)