Graphing Calculator For Trigonometry (20-1)

Question 1

How do you make sure your TI‑84/T184 is in degree mode before using trigonometric functions?

Answer 1

Press MODE, highlight Degrees, and select it. This ensures all trig functions interpret angles correctly.

Question 2

On a graphing calculator, what is the usual order for entering an angle and a trig function?

Answer 2

Enter the angle first, then the trig function key.

Example: 30 → SIN → Result: 0.5.

On my emulator I enter SIN then 30.

Question 3

How can you check if your memory of an exact trig ratio is correct using a calculator?

Answer 3

Convert your exact ratio to a decimal (e.g., √3/2 → 0.866). Then plug in the calculator: COS(30) → 0.866. If they match, your memory is correct.

Question 4

How do you find the inverse sine, cosine, or tangent of a number on a graphing calculator?

Answer 4

Use sin⁻¹, cos⁻¹, tan⁻¹.

Example: sin⁻¹(0.5) → 30° (make sure in degree mode).

Question 5

Given an angle between 0 and 360 degrees, how can you find the reference angle for any angle θ using a calculator?

Answer 5

Use subtraction formulas:
- Quadrant I: θ
- Quadrant II: 180 − θ
- Quadrant III: θ − 180
- Quadrant IV: 360 − θ
Type these directly into the calculator to get the decimal.

Question 6

How can you check coterminal angles on a graphing calculator?

Answer 6

Add or subtract multiples of 360° for degrees (or 2π for radians).

Example: 30° → 30+360=390°, 30−360=−330°. Enter these directly to see the same sine/cosine values.

Question 7

How do you quickly check which quadrants an angle is in if you have the reference angle and you know what trig ratio that reference angle came from?

Answer 7

Use COS, SIN, or TAN on the angle:
- Positive cosine → Quadrant I or IV
- Negative cosine → Quadrant II or III
- Positive sine → Quadrant I or II
- Negative sine → Quadrant III or IV

Question 8

How can you verify the ambiguous case when solving an SSA triangle?

Answer 8

Solve for the first angle using sin⁻¹. Then check the second possible angle: 180 − θ. Use the calculator to check if the angles make a valid triangle (sum < 180°).

Question 9

How do you solve for an unknown side using soh-cah-toa on a graphing calculator?

Answer 9

Enter the formula directly.

Example: hypotenuse = 10, angle = 30°, find opposite: 10*sin(30) → 5.

Question 10

How do you solve for an unknown angle using soh-cah-toa on a graphing calculator?

Answer 10

Enter the ratio, then use inverse function.

Example: opposite = 4, hypotenuse = 5 → θ = sin⁻¹(4/5) → θ ≈ 53.13°.

Question 11

How can you use your calculator to check exact ratios from 30°, 45°, and 60° triangles?

Answer 11

Memorize the exact value (like sin 60° = √3/2). Convert it to decimal: √3/2 → 0.866. Then plug SIN(60) into calculator → 0.866. If they match, you’re correct.

Question 12

How do you quickly convert between degrees and radians on a graphing calculator?

Answer 12

Use DRG or MODE to switch, or multiply: degrees × π/180 = radians.

Example: 90° → 90*π/180 = π/2.

Question 13

Practice card: Check if your memory of cos 30° is correct.

Answer 13

Calculate √3/2 → 0.866 in decimal. Enter COS(30) in degree mode → 0.866. Compare.

Question 14

Practice card: Verify the reference angle for 150° using your calculator.

Answer 14

180 − 150 = 30°. Enter SIN(30) → 0.5, compare with SIN(150) → 0.5.

Question 15

Practice card: Solve an SSA triangle on a calculator (A=40°, a=8, b=10). Check ambiguous case.

Answer 15

h = b*sinA
= 10sin40
≈ 6.427876

h < a < b so there will be two triangles

sin B = (bsin A)/a
= (10sin40)/8
≈ 0.6427876/8
≈ 0.8034845

B = sin⁻¹(0.8034845)
≈ 53.464°, 126.536°

check if A+B < 180° to confirm triangle validity. Notice that if you round too far that you cannot check this properly.

40°+126.536° = 166.536°

So both triangles are valid