1.3 Right Triangle Trigonometry

1. 1.3 Right Triangle Trigonometry Part 4

2. From Yeserday: Notice that sin 30° = ½ = cos 60°. This occurs because 30°and 60° are complementary.

3. The sum of all of the angles in a triangle always is 180° 90° What is the sum of  + ? Two angles whose sum is 90° are called complementary angles.  c opposite  adjacent to  b  a Since  and  are complementary angles and sin  = cos , sine and cosine are called cofunctions. adjacent to  opposite  This is where we get the name cosine, a cofunction of sine.

4. Looking at the names of the other trig functions can you guess which ones are cofunctions of each other? secant and cosecant tangent and cotangent Let's see if this is right. Does sec  = csc ? hypotenuse over adjacent hypotenuse over opposite  c opposite  adjacent to  b  a This whole idea of the relationship between cofunctions can be stated as: adjacent to  opposite  Cofunctions of complementary angles are equal.

5. Cofunctions of complementary angles are equal.

6. Remember  The sum of complementary angles in radians is since 90° is the same as Cofunctions of complementary angles are equal. cos 27° = sin(90° - 27°) = sin 63° Using the theorem above, what trig function of what angle does this equal? Let's try one in radians. What trig functions of what angle does this equal?

7. Classwork • 1.3 Worksheet - Cofunctions of Complementary Angles