Asked by Sydney
Evaluate: tan(arcsin(8/17)+ arctan(4/3))
I understand that I have to make triangles out of the values given-- with 15 being the other side of the 17 and 8 triangle, and 5 being the other side of the 4 and 3 triangle. I'm not sure where to go on from there, though.
I understand that I have to make triangles out of the values given-- with 15 being the other side of the 17 and 8 triangle, and 5 being the other side of the 4 and 3 triangle. I'm not sure where to go on from there, though.
Answers
Answered by
Jai
Yeah, you have to draw two different triangles for them. It's easier to solve this if you draw them.
Anyway, we let arcsin(8/17) be equal to some angle, A. And we let arctan(4/3) be equal to some angle, B. In your drawing of two triangles, label these angles as A and B.
We can rewrite the expression tan(arcsin(8/17)+ arctan(4/3)) as:
tan(A + B)
Using the formula for sum of tangents, we'll have its expanded for:
( tan(A) + tan(B) ) / ( 1 - tan(A)tan(B) )
Since you have your drawing of triangles, you now put values for each. From the drawing, we know that
tan A = 8/15, and
tan B = 4/3
substituting,
= ( 8/15 + 4/3 ) / ( 1 - 8/15 * 4/3 )
= 84/13
hope this helps~ `u`
Anyway, we let arcsin(8/17) be equal to some angle, A. And we let arctan(4/3) be equal to some angle, B. In your drawing of two triangles, label these angles as A and B.
We can rewrite the expression tan(arcsin(8/17)+ arctan(4/3)) as:
tan(A + B)
Using the formula for sum of tangents, we'll have its expanded for:
( tan(A) + tan(B) ) / ( 1 - tan(A)tan(B) )
Since you have your drawing of triangles, you now put values for each. From the drawing, we know that
tan A = 8/15, and
tan B = 4/3
substituting,
= ( 8/15 + 4/3 ) / ( 1 - 8/15 * 4/3 )
= 84/13
hope this helps~ `u`
Answered by
Sydney
Ah, that makes sense! I always forget the trig addition formulas, thank you!