3.3 Trigonometry

• What is the formula for the tangent ratio?

  $\tan \theta =$$\frac{\text{opposite}}{\text{adjacent}}$
• To find a missing side in a right-angled triangle, we can use trigonometric ratios.
• If the hypotenuse is 10 cm and the angle is 30°, the opposite side is 5 cm.


  True
• What is the formula for sine in a right-angled triangle?

  \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}</latex>
• Sine is defined as the ratio of the opposite side to the hypotenuse
• Trigonometric ratios can be used to find unknown side lengths or angles
• When finding the opposite side, if the hypotenuse and angle are known, you should use the sine ratio.
• What is the formula for sine in trigonometry?

  $\sin \theta =$$\frac{\text{opposite}}{\text{hypotenuse}}$
• Trigonometric ratios can be used to find missing sides or angles in right-angled triangles.


  True
• When calculating a missing side length, you must choose the trigonometric ratio that relates the known and unknown
• When solving for an unknown angle, you often use the inverse trigonometric function, such as $\tan^{ - 1}$
• To find the opposite side in a right-angled triangle, you can use the sine ratio.
• The tangent ratio relates the opposite side to the hypotenuse.

  False
• The cosine ratio relates the adjacent side to the hypotenuse.


  True
• Steps to calculate a missing side or angle in a right-angled triangle

  1️⃣ Identify given values and unknown

  2️⃣ Choose appropriate trigonometric ratio

  3️⃣ Set up equation using given values

  4️⃣ Solve for unknown value
• Steps to find a missing side length using trigonometric ratios

  1️⃣ Identify the given values and unknown

  2️⃣ Choose the appropriate trigonometric ratio

  3️⃣ Set up the equation using the given values

  4️⃣ Solve for the unknown value
• Match the step with its description in finding a missing angle using trigonometric ratios:

  Identify given values ↔️ Determine known side lengths

  Choose appropriate ratio ↔️ Relate known and unknown

  Set up equation ↔️ Plug in given values

  Solve for angle ↔️ Isolate unknown angle
• In construction, if the height of a building is 50 meters and the angle of elevation is 60°, the adjacent distance is 30
• Match the trigonometric identity with its formula:

  Reciprocal Identities ↔️ $\csc \theta =$$\frac{1}{\sin \theta}$, $\sec \theta =$$\frac{1}{\cos \theta}$, $\cot \theta =$$\frac{1}{\tan \theta}$

  Cofunction Identities ↔️ $\sin (\frac{\pi}{2} - \theta) =$$\cos \theta$, $\cos (\frac{\pi}{2} - \theta) =$$\sin \theta$

  Angle Addition Identities ↔️ $\sin (\theta \pm \phi) =$$\sin \theta \cos \phi \pm \cos \theta \sin \phi$
• What is the first step in solving problems involving trigonometric functions in right-angled triangles?

  Identify given values
• Trigonometric ratios can only be used in right-angled triangles


  True
• Trigonometric ratios allow us to find unknown side lengths or angles
• The tangent ratio is defined as the ratio of the opposite side to the hypotenuse

  False
• Steps to solve problems using trigonometric ratios

  1️⃣ Identify given values and unknown

  2️⃣ Choose appropriate trigonometric ratio

  3️⃣ Set up equation using given values

  4️⃣ Solve for unknown value
• The cosine ratio is the ratio of the adjacent side to the hypotenuse.


  True
• If $\sin 30° =$$\frac{\text{opposite}}{10}$, what is the length of the opposite side?


  5 cm
• Which trigonometric ratio should you use if you have the hypotenuse and want to find the opposite side?

  Sine
• Trigonometric ratios relate the known and unknown values
• What are the three trigonometric ratios in a right-angled triangle?

  Sine, cosine, tangent
• Tangent is the ratio of the opposite side to the adjacent side.

  True
• To find a missing side, you must first identify the known values and the unknown.


  True
• Match the trigonometric ratio with its formula:

  Sine ↔️ $\sin \theta =$$\frac{\text{opposite}}{\text{hypotenuse}}$

  Cosine ↔️ $\cos \theta =$$\frac{\text{adjacent}}{\text{hypotenuse}}$

  Tangent ↔️ $\tan \theta =$$\frac{\text{opposite}}{\text{adjacent}}$
• What is the formula for tangent in trigonometry?

  $\tan \theta =$$\frac{\text{opposite}}{\text{adjacent}}$
• What is the first step in calculating a missing side or angle using trigonometric ratios?

  Identify given values
• In trigonometry, what do you use when you are given the opposite and adjacent side lengths and need to find the unknown angle?

  Tangent
• What is the opposite side length in a right-angled triangle with a hypotenuse of 10 cm and an angle of 30°?

  5 cm
• What are the three trigonometric ratios used in right-angled triangles?

  Sine, cosine, tangent
• Steps to calculate a missing side or angle in a right-angled triangle

  1️⃣ Identify given values and unknown

  2️⃣ Choose appropriate trigonometric ratio

  3️⃣ Set up equation using given values

  4️⃣ Solve for unknown value
• What is the opposite side length if the hypotenuse is 10 cm and the angle is 30°?

  5 cm
• Trigonometric ratios can be used to find missing sides in right-angled triangles.


  True