Worksheet2A,2B,3

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Worksheet 2

RECALL:

I. 45° − 45° − 90° Triangle:

Note:

𝒆𝒂𝒄𝒉 𝒍𝒆𝒈 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝒆𝒂𝒄𝒉 𝒐𝒕𝒉𝒆𝒓

𝑻𝒉𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 = √𝟐 × 𝒍𝒆𝒈

NAME:

II. 30° − 60° − 90° Triangle:

Note:

𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 (𝒍𝒂𝒓𝒈𝒆𝒔𝒕 𝒔𝒊𝒅𝒆) = 𝟐 × 𝒔𝒎𝒂𝒍𝒍𝒆𝒔𝒕 𝒔𝒊𝒅𝒆

𝒎𝒆𝒅𝒊𝒖𝒎 𝒔𝒊𝒅𝒆 = √𝟑 × 𝒔𝒎𝒂𝒍𝒍𝒆𝒔𝒕 𝒔𝒊𝒅𝒆

Determine trig function values of an angle 𝜽. Step 1: Draw 𝜃 in standard position. Step 2: Pick a point on the terminal side of 𝜃, connect it to the x-axis. Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle

Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃

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Show step by step for the following problems. Determine 6 trig function

values of the following angle 𝜃.

1. 𝜃 = 0° Step 1: Draw 𝜃 in standard position.

Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis

Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle

Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃

cos (0°) = 𝑥

𝑟 =

𝑠𝑖𝑛 0° = 𝑦

𝑟 =

𝑡𝑎𝑛 0° = 𝑦

𝑥 =

𝑐𝑜𝑡 0° = 𝑥

𝑦 =

sec 0° = 𝑟

𝑥 =

csc 0° = 𝑟

𝑦 =

3

2. 𝜃 = 30° Step 1: Draw 𝜃 in standard position. Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis

Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃

cos (30°) = 𝑠𝑖𝑛 ( ) = 𝑡𝑎𝑛 ( ) = 𝑐𝑜𝑡 ( ) = sec ( ) = csc ( ) =

4

3. 𝜃 = 45° Step 1: Draw 𝜃 in standard position. Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis

Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃

cos (45°) = 𝑠𝑖𝑛 ( ) = 𝑡𝑎𝑛 ( ) = 𝑐𝑜𝑡 ( ) = sec ( ) = csc ( ) =

5

4. 𝜃 = 60° Step 1: Draw 𝜃 in standard position. Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis

Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃

cos (60°) = 𝑠𝑖𝑛 ( ) = 𝑡𝑎𝑛 ( ) = 𝑐𝑜𝑡 ( ) = sec ( ) = csc ( ) =

6

5. 𝜃 = 90°

Step 1: Draw 𝜃 in standard position. Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis

Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle

Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃

cos (90°) = 𝑠𝑖𝑛 ( ) = 𝑡𝑎𝑛 ( ) = 𝑐𝑜𝑡 ( ) = sec ( ) = csc ( ) =

7

6. 𝜃 = 120° Step 1: Draw 𝜃 in standard position. Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis

Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle

Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃

cos (120°) = 𝑠𝑖𝑛 ( ) = 𝑡𝑎𝑛 ( ) = 𝑐𝑜𝑡 ( ) = sec ( ) = csc ( ) =

8

7. 𝜃 = 135° Step 1: Draw 𝜃 in standard position. Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis

Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle

Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃

cos (135°) = 𝑠𝑖𝑛 ( ) = 𝑡𝑎𝑛 ( ) = 𝑐𝑜𝑡 ( ) = sec ( ) = csc ( ) =

9

8. 𝜃 = 150° Step 1: Draw 𝜃 in standard position. Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis

Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃

cos (150°) = 𝑠𝑖𝑛 ( ) = 𝑡𝑎𝑛 ( ) = 𝑐𝑜𝑡 ( ) = sec ( ) = csc ( ) =

10

9. 𝜃 = 180° Step 1: Draw 𝜃 in standard position. Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis

Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃

cos (180°) = 𝑠𝑖𝑛 ( ) = 𝑡𝑎𝑛 ( ) = 𝑐𝑜𝑡 ( ) = sec ( ) = csc ( ) =