if the measure of angle 0 is 3pi/4 which statements are true (multiple choice)
A. sin(0)=sqrt2/2
B. The measure of the reference angle is 45
C. The measure of the reference angle is 30
D. The measure of the reference angle is 60
E. cos(0)=sqrt2/2
F. tan(0)=1

if the measure of angle 0 is 3pi4 which statements are true multiple choice A sin0sqrt22 B The measure of the reference angle is 45 C The measure of the referen class=

Respuesta :

2 Answers:

Choice A

Choice B

===========================================================

Explanation:

Refer to the unit circle shown below.

The angle 3pi/4 radians is equivalent to 135 degrees.

The angle is in Q2.

The reference angle for stuff in Q2 is 180 - theta = 180 - 135 = 45 degrees. This makes choice B one of the answers.  It rules out choices C and D.

-----------

The terminal point for this angle is [tex]\left(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)[/tex] which those coordinates represent the cosine and sine of theta in that order.

[tex]x = \cos(\theta) = -\frac{\sqrt{2}}{2}\\\\y= \sin(\theta) = \frac{\sqrt{2}}{2}[/tex]

Dividing sine over cosine gets us [tex]\tan(\theta) = -1[/tex]

These facts show that choice A is the other answer. Choices E and F are false.

Ver imagen jimthompson5910