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### Course: Geometry (FL B.E.S.T.)>Unit 7

Lesson 8: Sine & cosine of complementary angles

# Using complementary angles

Sal solved the following problem: Given that cos(58°)=0.53, find sin(32°). Created by Sal Khan.

## Want to join the conversation?

• Would sin(45) also equal cos(45), since they are complementary angles?
• Yes, the two are the same thing
• What is does soh coh toa stand for?
thank you?
• SOH--> Sin ->Opposite/hypotenuse
• hi im in 8th grade, so this may sound stupid, but what exactly are the definitions of sine, cosine and tangent? I mean are they used in geomrtry, algebra, pre cal, etc.?
• The trig functions are ratios between the sides of a triangle. Yes, they are definitely used in Geometry and every math level above it.
• So what is the answer to the problem? What is sin 32 degrees?
• You never ever calculate sin/cos/tan by hand. However you will need know the values of 30, 45, 60 degrees which can be done by the special triangle.

If you need calculate sin 32 then you should use a calculator.
• Confused on all of the comments about sqrt- what exactly does that have to do with SOH CAH TOA and such?
• When you progress through the course a little more, you'll learn that since all similar triangles have the same trig values and the 30-60-90 and 45-45-90 have special side ratios, you can get the trig values of angles in these triangles.
For example, in a 30 - 60 - 90 triangle, the side lengths can be written as x - x*sqrt(3) - 2x. If we were to take the cosine of the 60 degree angle, we would take the side adjacent to the 60 degree angle and divide it by hypotenuse. This means we would get x / 2x. "x" cancels out, leaving us with cos(60 deg) = 1/2
• what would the tangent of the right angle be? the sin would be 1, and the cos would be be 0 (idk why, but i checked it on the calc and it said 0) but when i tried to calculate the tangent , it said invalid input
• The tangent is undefined for a 90° angle.
• If cos(58°)=0.53 does that mean that the ratio of BC/AB also equals 0.53? If so what does this tell us? I mean what is the significance of know how cos(58) evaluates?
• Yes to the first question, and it tells us that if we know either the length of the hypotenuse or the adjacent side, we can find the other one. It also tells us that all 32-58-90 triangles will have the same proportion for the cos no matter the size.
• What does SOH stand for?
(1 vote)
• SOH-CAH-TOA is an abbreviation to help you remember when to use cosine, sin, or tangent of an angle. So SOH would stand for Sin equals Opposite side of a triangle over the Hypotenuse of the triangle. CAH would stand for Cosine equals Adjacent side of a triangle over the Hypotenuse of the the triangle. And finally, TOA represents Tangent equals Opposite side of a triangle over the adjacent side of the triangle. You would take the angle you are focusing on, and then find the opposite side of that angle and hypotenuse side of the triangle and plug in those numbers for the sin of an angle (an example).

SOH-CAH-TOA is only used in right triangles
• While figuring out the sin, cos or tan of 90 deg, which side should we take as adjacent ? Because none of the sides that make the angle is the hypotenuse .
(1 vote)
• When using SOH CAH TOA, you must use a non-90 deg angle as your reference angle. Using the right angle with SOH CAH TOA creates a problem that you discovered -> the opposite side IS the hypotenuse and there is no way to distinguish between the two legs.

Use a different angle. If one isn't given, use inverse sine, cosine, or tangent with the two given sides to find it.