Confuses how my teacher got this?

posted by on .

The question says "Given that cos(theta)=(-7/25) and sin(theta)>0, calculate the exact values of tan(theta) and csc(theta).

We start out by drawing a triangle.
25 is on the side of the hypotenuse and -7 is on the adjacent side, because cos is adjacent over hypotenuse.

Somehow he gets to this halfway through: 225-49=176.
I can understand where he got the 49.
Probably from (-7)^2

I thought you had to use the equation
a^2+b^2=c^2 or
y^2+x^2=r^2
So it would be y^2 +(-7)^2=25^2
(-7)^2 is 49. Subtract this from 25^2, so we can get y^2 by itself.
Would that be going the right way?

I'm mainly just confused about how he got the 225?

• Confuses how my teacher got this? - ,

He ends up with the answers:
tan(theta)= (-square root of 176)/7 and
csc(theta)= (25 x square root of 176)/176

• Confuses how my teacher got this? - ,

Looks like either the hypotenuse is 15, so 15^2 = 225

or, he made a mistake and it should have been 625, rather than 225. I think this is the case, because then you have a 7-24-25 triangle.

• Confuses how my teacher got this? - ,

I think its the second one, but how did you get 625?

• Confuses how my teacher got this? - ,

He started out saying that cos = 7/25. That means that if the other leg i y, then
7^2 + y^2 = 25^2 = 625
y = 24