Answer to Question #122554 in Trigonometry for Lily

Question

Write tan (-1100) as a positive acute angle.
Give an exact value for Cos 120º.
If θ is an acute angle in standard position and B (-3, 4) is a point on the terminal side of the angle, what is the value of sin θ?
The line y=3x creates an acute angle θ when it crosses the x-axis. Find the exact value of sec θ?
Find the exact value of sin 1350.
Find the exact value of cosec 3000.
The value of Sin 3700 is equal to?
The value of Sin 4200 is equal to?
The value of Sin 4350 is equal to?

Answer 1

As we know tan(-x)= -tanx

So tan(-1100⁰) = -tan(1100⁰)

It can be written as -tan(6$\Pi$ + 20⁰)

Or -tan(20⁰)

Value of cos(120⁰)= -0.5

SinX= perpendicular/hypotenuse

=$Y/\sqrt{Y^2+X^2}$

SinX=4/5

Y=3X so slope is 3

tanx=3

x= 71.56⁰

So sec(71.56⁰)= 3.1626

$Sin(7\Pi+90⁰)$ =-sin(90⁰)

Sin(1350⁰)=-1

$Cosec(16\Pi+120⁰)$ = cosec(120⁰)

Cosec(3000⁰)=1.154

$Sin(20\Pi+100⁰)$ =sin(100⁰)

Sin(3700⁰)=0.9848

Sin($23\Pi+60⁰)$ = -sin(60⁰)

Sin(4200⁰)=-0.866

$Sin(24\Pi+30⁰)$ = sin30⁰

Sin(4350⁰)=0.5