quiz3-sol

# quiz3-sol - AMS 151 (Fall, 2009) Joe Mitchell Applied...

This preview shows pages 1–2. Sign up to view the full content.

AMS 151 (Fall, 2009) Joe Mitchell Applied Calculus I Quiz # 3 – Solution Notes 1. Evaluate the following expressions: (a). sin(cos 1 ( 5 11 )) = Draw a right triangle and let θ be one of the two angles that is not π/ 2. Then, θ = cos 1 ( 5 11 ) if the side adjacent to θ is of length 5 and the hypotenuse is of length 11. Then, the side opposite θ is of length 11 2 - 5 2 = 96. Thus, sin(cos 1 ( 5 11 )) = sin θ = 96 11 . (b). tan(cos 1 ( 3 2 )) = Draw a right triangle and let θ be one of the two angles that is not π/ 2. Then, θ = cos 1 ( 3 2 ) if the side adjacent to θ is of length 3 and the hypotenuse is of length 2. Then, the side opposite θ is of length 2 2 - 3 = 1. (In fact, we know that θ = π/ 6, 30 degrees.) Thus, tan(cos 1 ( 3 2 )) = tan θ = 1 3 . (c). cos( 40 π 3 ) = Note that 40 π 3 = 13 π + π 3 (i.e., it is 6.5 revolutions, plus an additional angle π/ 3 (60 degrees). Thus, cos( 40 π 3 ) = cos(4 π/ 3) =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/07/2010 for the course AMS 151 taught by Professor Zhang during the Fall '08 term at SUNY Stony Brook.

### Page1 / 2

quiz3-sol - AMS 151 (Fall, 2009) Joe Mitchell Applied...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online