Trigonometry Without a Calculator

[andie]

I need help with figuring out how to find the answers to these without a calculator:
sin(?/3)=
cos(?/3)=
tan(?/3)=
sin(?/2)=
cos(3?/2)=
tan(3?/2)=

I was told to look at a unit circle, and I looked one up, but I don't know how to use it.

 

[mmm4444bot]

I was told to look at a unit circle, and I looked one up, but I don't know how to use it.

I'm not sure what you looked at, but for this exercise the unit circle diagram would need to give the coordinates of the intersection points between the circle and the terminal rays for the angles drawn.

The x-coordinate is the cosine value, and the y-coordinate is the sine value.

For example, the angle Pi/3 has its vertex at the center of the circle, its initial ray along the positive x-axis, and its terminal ray intersecting the unit circle in Quadrant I.

The coordinates of this intersection point are (1/2, sqrt(3)/2).

So, you can read off cos(Pi/3) as 1/2 and sin(Pi/3) as sqrt(3)/2.

Let me know if you need a unit circle with the angles and coordinates listed.

 

[Loren]

?/3 = 60°. An equilateral triangle has all angles = 60°. Label each side "1". Cut it in half and you have a 30-60 degree right triangle. You should be able to figure out the ratios of the sides, having used the Pythagorean Theorem.

 

[Denis]

I was told to look at a unit circle, and I looked one up, but I don't know how to use it.

WHAT is a unit circle ?

 

[mmm4444bot]

There's a bunch of unit circles on THIS PAGE.

I like the one on THIS PAGE, too.

All students of trigonometry should memorize the sine and cosine values for 0, 30, 45, 60, and 90 degrees near the beginning of the course.

No exceptions!

If these values were memorized, then all of the exercises in this thread could be determined from them.