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2002-E: Trigonometry 2: Trigonometric Functions

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2002-E: Trigonometry 2: Trigonometric Functions

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We typically label angles by the Greek letter \( \theta \), pronounced "theta." Once we have singled out a particular angle, each side has a new name:

  • A is the opposite of \( \theta \).
  • B is the adjacent of \( \theta \).
  • C is the hypotenuse.
  • \( \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} \)
  • \( \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} \)
  • \( \tan \theta = \frac{\text{opposite}}{\text{adjacent}} \)

Whenever we know what an angle is, we can use the three trigonometric functions: the sine, the cosine, and the tangent. To remember these three formulas, we use the silly word "SOHCAHTOA," which stands for: "Sine is opposite over hypotenuse; cosine is adjacent over hypotenuse; tangent is opposite over adjacent."

Problems

In each case, use one of the trigonometric functions to solve for the unknown side. For full credit, you must write the formula before using it.

Variable in Denominator

In some trigonometry problems, the unknown variable will be located in the denominator! In this case, the most straightforward method is to first multiply both sides of the equation by the unknown variable, then solve for it:

Example:

$$ \require{enclose} 48 = \frac{76}{X} \\ 48 \cdot X = \frac{76}{\enclose{horizontalstrike}{X}} \cdot \enclose{horizontalstrike}{X} \\ 48 \cdot X = 76 \\ X = \frac{76}{48} = 1.583 $$

Solve for \( x \) in each of the problems below. Please give all answers to 4 significant figures of accuracy.

  1. \( 49 = \frac{65}{x} \)
  2. \( 66 = \frac{82}{x} \)
  3. \( 42 = \frac{25}{x} \)

Trigonometry Problems with Variable in Denominator

Saying the Names Right!

  1. How do you read out loud the following equation: \( \sin 90^{\circ} = 1 \).
  2. How do you read out loud the following equation: \( \cos 90^{\circ} = 0 \).
  3. How do you read out loud the following equation: \( \tan 45^{\circ} = 1 \).

Extra Practice

(Not required to receive full credit for this assignment.)

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