MPM 2 D Trigonometry PreAmble and Review History

MPM 2 D Trigonometry Pre-Amble and Review

History �Historically, trigonometry was developed for use in astronomy and geography, but scientists have been using it for centuries for other purposes, too. �Trig is used in physics, engineering, and chemistry. �Trig is used primarily in calculus (which is perhaps its greatest application), linear algebra, and statistics. �Since these fields are used throughout

Trigonometry �Trigonometry is concerned with the ratios of lengths of sides of triangles. �In similar triangles, the ratios of corresponding sides are equal to each other.

Trigonometry • No matter where T and S are chosen, these ratios are the same.

Trigonometry �For a given angle <ABC, the ratio TD is unique for that angle. BD �The same holds true for the ratios: BT and TD BD BT �These ratios help define the primary trig

Trigonometry • sin B = opposite/hypotenuse = AC/AB • cos B = adjacent/hypotenuse = BC/AB

Examples � 1) Use your calculator to evaluate the following to the nearest thousandth: (Check for DEG in calc) a) Sin 40 o b) cos 50 o c) sin 30 o tan 45 o d) � 2) Use your calculator to find the unknown angle to the tenth: a) sin T = 1 b) tan D = ½ c) cos M =

Examples �Write the trig ratios of sin A, cos A and tan A for triangle ABC, expressing each answer as a fraction in lowest terms. Plan: Step 1: Find c Step 2: Identify O, A, H Step 3: Write formulae for primary trig ratios Step 4: Sub in values and simplify!!

Examples � 4) A plane flies over level ground at an altitude of 800 m on approach to land. The tower indicates the angle of approach is 21. 5 o. What is the diagonal distance from the tower to the plane to the nearest metre? �Step 1: Draw a diagram and label it!! �Step 2: Choose the appropriate formula to solve for the required unknown.

Example 4 continued • We want PT which is the hypotenuse. 800 m is the opposite of the given angle: T. • Therefore: use sin T = O/H to solve. • sin T = O/H • sin 21. 5 o = 800/PT