Trigonometry Pre-Amble and Review MPM2D 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 the natural and social sciences, trig is a very useful subject to study.

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 ratios.

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

Examples 1) Use your calculator to evaluate the following to the nearest thousandth: (Check for DEG in calc) a) Sin 40o b) cos 50o c) sin 30o d) tan 45o 2) Use your calculator to find the unknown angle to the tenth: a) sin T = 1 b) tan D = ½ c) cos M = ¼

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 21.5o. 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 21.5o = 800/PT PT = 2183 m

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