Section+1-6

=1.6 RightTriangle Trigonometry=

= =

**__Inverse Trigometric Funcitons__**

 * Terms**:


 * Inverse Sine:** sin-1(x)=a provided sina=x and -90<a<90
 * Inverse Cosine:** cos-1(x)=a provided cosa=x and 0<a<180
 * Inverse Tangent:** tan-1(x)=a provided tana =x and -90<a<90


 * Example:**

The sin30 = (1/2) and 30 is between or equal to -90 and 90 so the sin-1(1/2) = 30 The cos120=(1/2) and 120 is between or equal to 0 and 180 so the cos-1(1/2)=30 The tan45=1 and 45 is between -90 and 90 so so the tan-1(1)=45


 * __Right Triangles__**

Trigonometric Functions of an Acute Angle of a Right Triangle:**
 * Terms:

sin a = opp/hyp csc a = hyp/opp

cos a = adj/hyp sec a = hyp/adj

tan a = opp/adj cot a = adj/ opp



In the right triangle to the left you can see the hyp is 25 which was solved by using the pythagorean theorm 7² + 24² = c². Now after finding all of the sides of the triangle we have to find the 6 trigometric functions. To find the sina we have to find opp/hyp which is 7/25. To find the cosa we have to find adj/hyp which is 24/25. Finally to find the tana we have to find opp/adj which is 7/24. After doing that we have to find the other 3 trigometric functions. All you do is flip the sin to find the csca which is 25/7, flip the cos to find the seca which is 25/24, and flip the tan to find the cota which is 24/7.


 * __Height of an object__**

To find the height of this object you have to solve for A. In the triangle H = 120 and a is is a 35° anlge. So A equals 120 multiplied by the sin 35 because it is the opposite angle of A. After doing the math you get A to equal 68.83 feet. 