# Trignonmetry

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Tan(-3p/4)=

Sec(2p/3)=

Csc(7p/4)=

Cot(11p/6)=

p=pie

• Trignonmetry -

-3pi/4 = 2pi -3pi/4 = + 5 pi/4
so you really want tan 5pi/4 which is pi/4 below the -y axis
x = -1
y = -1
y/x = tangent = 1

sec 2 pi/3 = 1/cos 2 pi/3
that angle is between pi/2 and pi, second quadrant
pi - 2 pi/3 = pi/3 above -y axis
x = -1
y = +sqrt 3
sqrt(x^2+y^2) = hypotenuse = 2
so
cos(2pi/3) = -1/2
sec(2 pi/3)= -2

etc. draw the triangles

• Trignonmetry -

You should be familiar with the trig ratios of the 30-60-90º triangle as well as the 45-45-90º triangle

all your given angles are multiples of these.

I will do the last one
cot(11pi/6) = 1/tan(11pi/6)

11pi/6 is in the fourth quadrant, in the fourth quadrant the tangent is negative, so the cotangent is negative.

The angle is pi/6 away from the x-axis, so the 'angle in standard position' is pi/6
tan pi/6 = 1/√3, so cot pi/6 = √3

then cot(11pi/6) = -√3

do the others the same way.

• Trignonmetry -

What is sin of 660?
And
What is csc(-2pi)/3?

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