3.6 E: Trigonometry

• Which type of triangles is trigonometry most commonly applied to?

  Right-angled triangles
• The acronym SOH CAH TOA helps in remembering the trigonometric ratios.


  True
• In SOH CAH TOA, CAH stands for Cosine = Adjacent / Hypotenuse
• What is the formula for sine (sin) in a right-angled triangle?

  \sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}}</latex>
• The acronym SOH CAH TOA helps in remembering the trigonometric functions and their formulas.


  True
• In SOH CAH TOA, TOA represents Tangent = Opposite / Adjacent
• What is the reciprocal identity for sine (sin)?

  \sin \theta = \frac{1}{\csc \theta}</latex>
• Trigonometric identities are useful for simplifying trigonometric expressions.


  True
• Why are trigonometric identities used in solving trigonometric equations?

  To simplify the equation
• Which trigonometric identity can be used to simplify $\sin^{2} \theta +$$\cos^{2} \theta =$$1$?


  Pythagorean identity
• Trigonometric identities can be used to simplify trigonometric equations.


  True
• Which trigonometric identity is commonly used to simplify equations?

  $\sin^{2} \theta +$$\cos^{2} \theta =$$1$
• What are the solutions for $\sin \theta =$$\frac{1}{2}$ in the domain [0°, 360°]?


  30°, 150°, 210°, 330°
• The sine function is defined as opposite over hypotenuse
• What does TOA stand for in the acronym SOH CAH TOA?

  Tangent = Opposite / Adjacent
• What is the first strategy for solving trigonometric equations?

  Isolate the trigonometric function
• The identity $\sin^{2} \theta +$$\cos^{2} \theta =$$1$ can be used to simplify trigonometric equations.


  True
• The period of the sine and cosine graphs is $2\pi$.


  True
• The tangent graph has vertical asymptotes at odd multiples of $\frac{\pi}{2}$.


  True
• What is the amplitude of $y =$$2 \sin(3x)$?


  2
• Match the trigonometric ratio with its definition:

  Sine (sin) ↔️ Opposite / Hypotenuse

  Cosine (cos) ↔️ Adjacent / Hypotenuse

  Tangent (tan) ↔️ Opposite / Adjacent
• The cosine of an angle is defined as adjacent over hypotenuse.

  True
• What are the sine and cosine rules used for in trigonometry?

  Finding sides and angles
• Under what conditions is the cosine rule used in trigonometry?

  All three sides known
• The acronym SOH CAH TOA is used to remember the trigonometric ratios.
• The three key trigonometric ratios are sine, cosine, and tangent
• What is the formula for cosine (cos) in terms of triangle sides?

  $\cos \theta =$$\frac{\text{Adjacent}}{\text{Hypotenuse}}$
• In SOH CAH TOA, SOH stands for Sine = Opposite / Hypotenuse
• In SOH CAH TOA, TOA stands for Tangent = Opposite / Adjacent
• What is the formula for cosine (cos) in a right-angled triangle?

  $\cos \theta =$$\frac{\text{Adjacent}}{\text{Hypotenuse}}$
• In SOH CAH TOA, SOH represents Sine = Opposite / Hypotenuse
• What is the Pythagorean identity relating sine and cosine?

  $\sin^{2} \theta +$$\cos^{2} \theta =$$1$
• What is the reciprocal identity for cosine (cos)?

  $\cos \theta =$$\frac{1}{\sec \theta}$
• What is the quotient identity for tangent (tan)?

  $\frac{\sin \theta}{\cos \theta} =$$\tan \theta$
• Solving trigonometric equations involves finding the values of the angle θ that satisfy the equation
• For the equation $\sin \theta =$$\frac{1}{2}$, the solutions within the domain $0^\circ \leq \theta \leq 360^\circ$ are 30° and 150°.


  True
• Steps for solving a trigonometric equation

  1️⃣ Isolate the trigonometric function

  2️⃣ Use trigonometric identities to simplify

  3️⃣ Find all possible solutions within the domain
• To solve \sin \theta = \frac{1}{2}</latex>, the solutions in the domain [0°, 360°] are 30° and 150°
• When solving trigonometric equations, you must find all possible solutions within a given domain
• Match the trigonometric ratio with its definition:

  Sine (sin) ↔️ Opposite / Hypotenuse

  Cosine (cos) ↔️ Adjacent / Hypotenuse

  Tangent (tan) ↔️ Opposite / Adjacent