1.5 Trigonometry

• Arrange the SOH CAH TOA acronym in the correct order:

  1️⃣ SOH

  2️⃣ CAH

  3️⃣ TOA
• Cosine is defined as Adjacent / Hypotenuse.


  True
• Sine, Cosine, and Tangent are the three primary trigonometric functions
• What is the ratio for sine in a right-angled triangle?

  Opposite / Hypotenuse
• What is the radius of the unit circle?

  1
• What are trigonometric identities used for?

  Simplifying expressions
• The reciprocal identity for csc θ is $\frac{1}{\sin \theta}$
• Trigonometric identities are true for all values of the variable for which the expressions are defined.


  True
• What is the ratio for $\cos \theta$ in a right-angled triangle?


  $\frac{\text{Adjacent}}{\text{Hypotenuse}}$
• What is the Quotient identity for $\tan \theta$?


  $\tan \theta =$$\frac{\sin \theta}{\cos \theta}$
• What is the Quotient identity for $\tan \theta$?


  $\tan \theta =$$\frac{\sin \theta}{\cos \theta}$
• What is the first step in solving trigonometric equations?

  Isolate the function
• What does the amplitude of a trigonometric graph represent?

  Maximum displacement
• The period of the graph y = 2sin(2x - π) is \pi
• What transformations are applied to the graph y = sin(x) to obtain y = 2sin(2x - π)?

  Vertical stretch, horizontal compression, right shift
• In the unit circle, the y-coordinate of a point at angle θ is equal to sin θ.

  True
• Match the trigonometric transformation with its effect on the graph:

  Amplitude Change ↔️ Stretches or compresses vertically

  Period Change ↔️ Stretches or compresses horizontally

  Phase Shift ↔️ Shifts the graph horizontally
• What happens to the amplitude of the graph y = sin x when it is transformed to y = 2sin(2x - π)?

  Stretched vertically by 2
• The unit circle is a circle with a radius of 2.

  False
• Match the trigonometric function with its ratio in a right-angled triangle:

  Sine (sin θ) ↔️ Opposite / Hypotenuse

  Cosine (cos θ) ↔️ Adjacent / Hypotenuse

  Tangent (tan θ) ↔️ Opposite / Adjacent
• Sine, Cosine, and Tangent define ratios of sides in a right-angled triangle relative to an angle
• Match the trigonometric function with its relationship to the unit circle:

  Sine (sin θ) ↔️ y-coordinate

  Cosine (cos θ) ↔️ x-coordinate

  Tangent (tan θ) ↔️ Slope
• The Pythagorean identity is \sin^{2} \theta + \cos^{2} \theta = 1</latex>


  True
• What is the value of $\sin 30°$ using the unit circle?


  $\frac{1}{2}$
• What are the key steps in solving trigonometric equations?

  Isolate function, reference angles, periodicity
• Arrange the steps in relating the unit circle to trigonometric functions:

  1️⃣ Define the unit circle

  2️⃣ Understand sine as y-coordinate

  3️⃣ Understand cosine as x-coordinate

  4️⃣ Understand tangent as slope
• The Pythagorean identity can be used to simplify expressions such as $\sin^{2} \theta +$$\cos^{2} \theta$ to 1.


  True
• Using the Pythagorean identity, $\sin^{2} \theta +$$\cos^{2} \theta$ can be simplified to 1.


  True
• How is the general solution for $\sin \theta =$$\alpha$ expressed using periodicity?


  $\theta =$$\alpha +$$2n\pi$
• The amplitude of $y =$$2\sin(2x - \pi)$ is 2.


  True
• Match the trigonometric function with its ratio:

  Sine (sin θ) ↔️ $\frac{\text{Opposite}}{\text{Hypotenuse}}$

  Cosine (cos θ) ↔️ $\frac{\text{Adjacent}}{\text{Hypotenuse}}$

  Tangent (tan θ) ↔️ $\frac{\text{Opposite}}{\text{Adjacent}}$
• In the unit circle, the x-coordinate of a point at angle θ is equal to cos θ
• The period of the graph y = 2sin(2x - π) is \pi
• The period of the graph y = 2sin(2x - π) is \pi
• At θ = 30°, sin 30° equals 1/2
• What is the quotient identity for tan θ?

  $\frac{\sin \theta}{\cos \theta}$
• What is the quotient identity for $\tan \theta$?


  $\frac{\sin \theta}{\cos \theta}$
• The general solution for $\sin \theta =$$\frac{1}{2}$ includes $\theta =$$\frac{\pi}{6} +$$2n\pi$.


  True
• What does the y-coordinate on the unit circle represent?

  $\sin \theta$
• What is the purpose of trigonometric identities?

  Simplify expressions