4 ESO Academics - Unit 07 - Exercises 4.7.2 -Trigonometric Ratios.

1. UNIT 07 February
1. Find the height of an equilateral triangle of side 5 cm without using Pythagoras´
Theorem.
2. Find 𝜶𝜶 in the first quadrant:
𝒂𝒂) 𝒔𝒔𝒊𝒊 𝒊𝒊 𝜶𝜶 =
√𝟑𝟑
𝟐𝟐
𝒃𝒃) 𝒄𝒄𝒐𝒐𝒐𝒐 𝜶𝜶 =
𝟏𝟏
𝟑𝟑
3. Without using calculator, write the sign of the trigonometric ratios of:
𝒂𝒂) 𝟑𝟑𝟏𝟏𝟏𝟏°
𝒃𝒃) 𝟐𝟐𝟐𝟐𝟐𝟐°
𝒄𝒄) 𝟐𝟐𝟕𝟕𝟕𝟕°
𝒅𝒅) 𝟐𝟐𝟗𝟗𝟓𝟓°
𝒆𝒆) 𝟕𝟕𝟎𝟎°
𝒇𝒇)𝟏𝟏𝟓𝟓𝟓𝟓°
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.7.2.1

2. UNIT 07 February
4. Reduce the trigonometric ratios to the first quadrant and calculate them:
𝒂𝒂) 𝒔𝒔𝒔𝒔𝒔𝒔 𝟐𝟐𝟐𝟐𝟐𝟐°
𝒃𝒃) 𝒄𝒄𝒐𝒐𝒐𝒐 𝟏𝟏𝟏𝟏𝟏𝟏°
𝒄𝒄) 𝒔𝒔𝒔𝒔𝒔𝒔 𝟑𝟑𝟎𝟎𝟎𝟎°
𝒅𝒅) 𝒄𝒄𝒐𝒐𝒐𝒐 𝟑𝟑𝟏𝟏𝟏𝟏°
5. Calculate the trigonometric ratios of 65°, 155° and 335° knowing that:
𝒔𝒔𝒔𝒔𝒔𝒔 𝟐𝟐𝟐𝟐 ° = 𝟎𝟎. 𝟒𝟒𝟒𝟒 𝒄𝒄𝒐𝒐𝒐𝒐 𝟐𝟐𝟐𝟐° = 𝟎𝟎. 𝟗𝟗𝟗𝟗 𝒕𝒕𝒂𝒂𝒂𝒂 𝟐𝟐𝟓𝟓° = 𝟎𝟎. 𝟒𝟒𝟕𝟕
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.7.2.2

3. UNIT 07 February
6. Find the trigonometric ratios of this angles finding a similar angle between 0°
and 360°:
𝒂𝒂) 𝟑𝟑𝟗𝟗𝟗𝟗°
𝒃𝒃) 𝟒𝟒𝟖𝟖𝟎𝟎°
𝒄𝒄) 𝟓𝟓𝟖𝟖𝟖𝟖°
𝒅𝒅) 𝟒𝟒𝟒𝟒𝟒𝟒°
𝒆𝒆) 𝟔𝟔𝟗𝟗𝟗𝟗°
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.7.2.3

4. UNIT 07 February
𝒇𝒇) − 𝟏𝟏, 𝟏𝟏𝟏𝟏𝟏𝟏°
𝒈𝒈) − 𝟏𝟏, 𝟎𝟎𝟎𝟎𝟎𝟎°
7. Find a couple of angles bigger than 360° and a couple negative angles that have
the same trigonometric ratios. Calculate this trigonometric ratios and reduce to
the first quadrant.
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.7.2.4