Trigonometry Study Guide PDF

Trigonometry Study Guide Ratios in Right Triangles ○ Hypotenuse: the side opposite the right angle. The hypotenuse, as noted below, is the longest side of a right triangle ○ The other two sides of a right triangle are the opposite and adjacent sides. These sides are...

Trigonometry Study Guide Ratios in Right Triangles ○ Hypotenuse: the side opposite the right angle. The hypotenuse, as noted below, is the longest side of a right triangle ○ The other two sides of a right triangle are the opposite and adjacent sides. These sides are labeled in relation to an angle ○ The opposite side of a triangle is the side across from a given angle ○ The adjacent side of a triangle is the non-hypotenuse side that is located next to a given angle Ratios in Right Triangles (continued)  ○ Congruent: Two triangles are congruent if they have the exact same size and shape - triangles are congruent if their corresponding angles are equal, and their corresponding sides have the same lengths ○ If two right triangles share an acute angle measure, they are similar by angle- angle similarity. ○ The ratios of corresponding side lengths within the triangles are equal. The ratio of the side lengths of a right triangle relies on one acute angle measure. ○ The Pythagorean theorem can be used to find any missing side length of a right triangle as long as you know the other two lengths. However, now we can relate angle measures to the right triangle side lengths. ○ This allows us to find both missing side lengths when we only know one length and an acute angle measure. The acute angle measures in a right triangle can be found based on any two side lengths. Introduction to the Trigonometric Ratios  To help using the ratios - remember: SOH CAH TOA ○ SIN = OPPOSITE / HYPOTENUSE ○ COS = ADJACENT / HYPOTENUSE ○ TAN = OPPOSITE / ADJACENT Solving for a Side Within a Right Triangle Using the Trigonometric Ratios  1: Determine which trigonometric ratio to use. 2: Create an equation using the trig ratio sine and then solve for the unknown. Solving for a Side Within a Right Triangle Using the Trigonometric Ratios (continued) Inverse Trig Functions ○ Inverse sine (sin ^−1) does the opposite of the sine.  ○ Inverse cosine (cos ^−1) does the opposite of cosine ○ Inverse tangent tan (tan ^−1) does the opposite of tan Sin ^-1 (x) is also called arcsin(x) 1/ sin x is also called csc(x) ○ EXAMPLE : Sine and Cosine of Complementary Angles Pythagorean Trig identity: used to figure out the value of (mostly) the hypotenuse in a right triangle. A and b sides are the two "non-hypotenuse" sides of the triangle (Opposite and Adjacent sides). ○ a^2 + b^2 = c^2  These triangles can be 45-45-90 triangles or 30-60-90 triangles. Quadrants  REMEMBER: “ALL STUDENTS TAKE CALCULUS” Modeling with Right Triangles Solving for a side  ○ Given the measure of angle B = 40 degrees, and the length of the hypotenuse, and find the side opposite to angle B, the trigonometric ratio that contains both of these sides is the sine: ○ CALCULATE: sin(