bbygrl1996: If sin (30) = 1⁄2 then the cosine of what angle will be 1⁄2?
Walt's method will work fine. Thankyou for posting Walt, you gave a good answer,
But there are other methods that I would like to talk about.
I'd really like other people who have been introduced to trigonometry at school to also pay attention to this one.
Draw a right angled triangle.
I really want you to do this. mark one angle as 30degrees
since sine 30 = 1/2
You can put 1 on the opposite side and 2 on the Hypotenuse.
Now think for a bit.......
Can you 'see' the answer yet? That is cos of what angle = 1/2
If not maybe you should work out what the 3rd angle will be.
what is the cos of the 3rd angle?
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Now we'll do it more generally
right angled triangle.JPG
Consider this triangle.
what is the size of the 3rd angle (in terms of theta)
hopefully you wil realise that it is 90-theta
Now, on this triangle,
what is Sine (theta)
hopefully you know that it is t / Hyp
what is Cosine(90 - theta) answer t / Hyp
so
sine (theta) = cosine (90-theta)
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Did you ever think about why cosine is sine with a co out the front?
Have you heard of COMPLEMENTARY ANGLES.
These are angles that add up to 90degrees
e.g. 30degrees and 60degrees are complementary angles
85 degrees and 5 degrees are complementary angles
The 'co' stands for complementary.
sine(theta) = cos(90-theta)
sin
-1 (t / H) + cos
-1(t/H) = 90 degrees
I hope that a few people learn something from this one
+118654 
