Trigonometry – Sine & Cosine – Angles – Demonstration

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1 Trigonometry – Sine & Cosine – Angles – Demonstration
This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

2 θ Hypotenuse Opposite Adjacent A right-angled triangle has 4 parts.
θ = Theta is either angle. Hypotenuse Opposite θ Adjacent Hypotenuse – always opposite the right-angle & always longest. Opposite – always opposite θ. Adjacent – next to θ.

3 SOH CAH 𝑥 (H) 13 cm 11 cm (O) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 O H A H
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 Label the sides. Choose the ratio. Write the formula. Substitute & calculate. O Sin θ H A Cos θ H Find the value of 𝑥 to 2dp. We want to find Sin θ. (so cover Sin θ) (H) 𝑆𝑖𝑛 θ= 𝑂 𝐻 𝑆𝑖𝑛 𝑥= 11 13 13 cm 𝑥 𝑆𝑖𝑛 − 𝑥= =57.80° (O) 11 cm

4 SOH CAH 𝑥 (O) 8 cm 10 cm (H) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 O H A H
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 Label the sides. Choose the ratio. Write the formula. Substitute & calculate. O Sin θ H A Cos θ H Find the value of 𝑥 to 2dp. We want to find Sin θ. (so cover Sin θ) (O) 8 cm 𝑆𝑖𝑛 θ= 𝑂 𝐻 𝑆𝑖𝑛 𝑥= 8 10 𝑥 10 cm 𝑆𝑖𝑛 − 𝑥= =53.13° (H)

5 SOH CAH 𝑥 8 cm 3 cm (H) (O) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 O H A H
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 Label the sides. Choose the ratio. Write the formula. Substitute & calculate. O Sin θ H A Cos θ H Find the value of 𝑥 to 2dp. We want to find Sin θ. (so cover Sin θ) 𝑥 𝑆𝑖𝑛 θ= 𝑂 𝐻 𝑆𝑖𝑛 𝑥= 3 8 8 cm 𝑆𝑖𝑛 − 3 cm (H) 𝑥= =22.02° (O)

6 SOH CAH 𝑥 (A) 3 cm 5 cm (H) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 O H A H
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 Label the sides. Choose the ratio. Write the formula. Substitute & calculate. O Sin θ H A Cos θ H Find the value of 𝑥 to 2dp. We want to find Cos θ. (so cover Cos θ) (A) 𝐶𝑜𝑠 θ= 𝐴 𝐻 𝐶𝑜𝑠 𝑥= 3 5 3 cm 𝑥 𝐶𝑜𝑠 − 5 cm 𝑥= =53.13° (H)

7 SOH CAH 𝑥 (H) 6 cm 4 cm (A) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 O H A H
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 Label the sides. Choose the ratio. Write the formula. Substitute & calculate. O Sin θ H A Cos θ H Find the value of 𝑥 to 2dp. We want to find Cos θ. (so cover Cos θ) (H) 6 cm 𝐶𝑜𝑠 θ= 𝐴 𝐻 𝐶𝑜𝑠 𝑥= 4 6 𝑥 𝐶𝑜𝑠 − 𝑥= =48.19° 4 cm (A)

8 SOH CAH 𝑥 (H) 7 cm 6 cm (A) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 O H A H
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 Label the sides. Choose the ratio. Write the formula. Substitute & calculate. O Sin θ H A Cos θ H Find the value of 𝑥 to 2dp. We want to find Cos θ. (so cover Cos θ) (H) 7 cm 𝐶𝑜𝑠 θ= 𝐴 𝐻 𝐶𝑜𝑠 𝑥= 6 7 𝑥 𝐶𝑜𝑠 − 6 cm 𝑥= =31.00° (A)

9 SOH CAH 𝑥 14 cm (H) 12 cm (O) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 O H A H
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 Label the sides. Choose the ratio. Write the formula. Substitute & calculate. O Sin θ H A Cos θ H Find the value of 𝑥 to 2dp. We want to find Sin θ. (so cover Sin θ) 𝑥 14 cm 𝑆𝑖𝑛 θ= 𝑂 𝐻 𝑆𝑖𝑛 𝑥= 12 14 (H) 𝑆𝑖𝑛 − 𝑥= =59.00° 12 cm (O)

10 SOH CAH 𝑥 (A) 4 cm 7 cm (H) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 O H A H
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 Label the sides. Choose the ratio. Write the formula. Substitute & calculate. O Sin θ H A Cos θ H Find the value of 𝑥 to 2dp. We want to find Cos θ. (so cover Cos θ) 4 cm (A) 𝐶𝑜𝑠 θ= 𝐴 𝐻 𝐶𝑜𝑠 𝑥= 4 7 𝑥 𝐶𝑜𝑠 − 7 cm 𝑥= =55.15° (H)

11 SOH CAH 𝑥 (H) 9 cm 8 cm (O) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 O H A H
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 Label the sides. Choose the ratio. Write the formula. Substitute & calculate. O Sin θ H A Cos θ H Find the value of 𝑥 to 2dp. We want to find Sin θ. (so cover Sin θ) (H) 9 cm 𝑆𝑖𝑛 θ= 𝑂 𝐻 𝑆𝑖𝑛 𝑥= 8 9 𝑥 𝑆𝑖𝑛 − 8 cm 𝑥= =62.73° (O)

12 SOH CAH 𝑥 (A) 15 cm 17 cm (H) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 O H A H
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 Label the sides. Choose the ratio. Write the formula. Substitute & calculate. O Sin θ H A Cos θ H Find the value of 𝑥 to 2dp. We want to find Cos θ. (so cover Cos θ) (A) 𝐶𝑜𝑠 θ= 𝐴 𝐻 𝐶𝑜𝑠 𝑥= 15 17 15 cm 𝑥 𝐶𝑜𝑠 − 17 cm 𝑥= =28.07° (H)

13 SOH CAH 𝑥 𝑥 𝑥 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 O H A H Cos θ Sin θ
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 Label the sides. Choose the ratio. Write the formula. Substitute & calculate. O Sin θ H A Cos θ H Calculate 𝑥 for these three triangles. (2dp) 9 cm 𝑥 𝑥 5 cm 7 cm 9 cm 8 cm 𝑥 11 cm

14 SOH CAH 𝑥 𝑥 𝑥 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 O H A H Cos θ Sin θ
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 Label the sides. Choose the ratio. Write the formula. Substitute & calculate. O Sin θ H A Cos θ H Calculate 𝑥 for these three triangles. (2dp) 9 cm 𝑥 𝑥 𝑆𝑂𝐻 5 cm 7 cm 9 cm 8 cm 𝑆𝑂𝐻 𝑥 𝐶𝐴𝐻 11 cm

15 SOH CAH 𝑥 𝑥 𝑥 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 O H A H 𝑥=39.52° 𝑥=33.75°
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 Label the sides. Choose the ratio. Write the formula. Substitute & calculate. O Sin θ H A Cos θ H Calculate 𝑥 for these three triangles. (2dp) 9 cm 𝑥=39.52° 𝑥 𝑥 𝑆𝑂𝐻 5 cm 7 cm 9 cm 8 cm 𝑆𝑂𝐻 𝑥 𝐶𝐴𝐻 𝑥=33.75° 11 cm 𝑥=27.27°

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