Question

Evaluate sin (-840) without using a calulator.
My answer is (-1/2) but i'm not too good with these so can someone please check it? Thanks:)

Answer 1

sin(-840) = -sin(840) .... since sine is an odd function


sin(-840) = -sin(480) .... 480 and 840 are coterminal angles


sin(-840) = -sin(120) ... 480 and 120 are coterminal angles


sin(-840) = -sqrt(3)/2 ... use the unit circle (link given below) to find this value


So the answer is sin(-840) = -sqrt(3)/2


Unit Circle: http://www.math.ucsd.edu/~jarmel/math4c/Unit_Circle_Angles.png

Answer 2

Thank you! I figured it out my mistake and then you posted this! I have memorize all the unit circle... :( Thank you so much anyways! Is the answer to sec (-15 pi/4) = sqrt 2/2 ?

Answer 3

sec(-15pi/4) = 1/cos(-15pi/4)


sec(-15pi/4) = 1/cos(15pi/4) ... Note: cosine is an even function


sec(-15pi/4) = 1/cos(-pi/4) ... 15pi/4 is coterminal with -pi/4


sec(-15pi/4) = 1/cos(pi/4)


sec(-15pi/4) = 1/(sqrt(2)/2) ... Use the unit circle here


sec(-15pi/4) = 1*(2/sqrt(2))


sec(-15pi/4) = 2/sqrt(2)


sec(-15pi/4) = (2/sqrt(2))*(sqrt(2)/sqrt(2)) ... Rationalizing the denominator


sec(-15pi/4) = (2*sqrt(2))/(sqrt(2)*sqrt(2))


sec(-15pi/4) = (2*sqrt(2))/(sqrt(2*2))


sec(-15pi/4) = (2*sqrt(2))/(sqrt(4))


sec(-15pi/4) = (2*sqrt(2))/(2)


sec(-15pi/4) = sqrt(2)



So the answer is sec(-15pi/4) = sqrt(2)

Answer 4

Thank you so much anyways! Is the answer to sec (-15 pi/4) = sqrt 2/2 ?

You found the cos(-15 pi/4) . Do you know how you went wrong?

Answer 5

btw, for sin(-840), I would keep adding 360 until I get to a number I like
-840+ 2*360= -120 or -120+360= 240
of course -120 and 240 are the same angle.