Please help, trig is a real problem for me

2. cotФ =

3. sec²Ф - tan²Ф = 1

4. = cos²∝

5. The value of sin x is

6. cos 15° =  

7. tan(α + β) =

8. sin(π - Ф) = sin Ф

9. cos 2Ф =

10. sin 2Ф = 0.96

Step-by-step explanation:

2.

∵ cos Ф =

∵ 90° < Ф < 180°

- That means Ф lies on the 2nd quadrant

∴ sin Ф is a positive value

∵ sin²Ф + cos²Ф = 1

∴ sin²Ф + ( )² = 1

∴ sin²Ф +   = 1

- Subtract from both sides  

∴ sin²Ф =  

- Take √ for both sides

∴ sinФ =

∵ cotФ = cosФ ÷ sinФ

∴ cotФ = ÷  

∴ cotФ =

3.

The expression is sec²Ф - tan²Ф

∵ tan²Ф = sec²Ф - 1

- Substitute tan²Ф by the right hand side in the expression

∴ sec²Ф - tan²Ф = sec²Ф - (sec²Ф - 1)

∴ sec²Ф - tan²Ф = sec²Ф - sec²Ф + 1

- Simplify the right hand side

∴ sec²Ф - tan²Ф = 1

4.

The expression is  

∵ The numerator is sin²∝ + cos²∝

∵ sin²∝ + cos²∝ = 1

∴ The numerator = 1

∵ The denominator is tan²∝ + 1

∵ tan²∝ =

∴ tan²∝ + 1 =   + 1

- Change 1 to  fraction

∴ tan²∝ + 1 =   +  

- Add the two fractions  

∴ tan²∝ + 1 =  

∵ sin²∝ + cos²∝ = 1

∴ tan²∝ + 1 =

∴ The denominator =  

∴   =

- Remember denominator the denominator will be a numerator

∴ = cos²∝

5.

∵ tan x cos x =

∵ tan x =

∴ × cos x =

- Simplify it by canceling cos x up with cos x down

∴ sin x =

∴ The value of sin x is

6.

∵ cos(Ф - ∝) = cosФ cos∝ + sinФ sin∝

∵ 45 - 30 = 15

∴ cos 15° = cos(45 - 30)°

- Use the rule above to find the exact value

∵ cos(45 - 30)° = cos 45° cos 30° + sin 45° sin 30°

∵ cos 45° = and sin 45° =

∵ cos 30° = and sin 30° =

∴ cos(45 - 30)° =   ×   +  

∴ cos(45 - 30)° =   +    =

∴ cos 15° =  

7.

∵ tan(α + β) =

∵ cos α = and 0° < α < 90°

- That means α is in the 1st quadrant, then all trigonometry

    ratios are positive

∵ sin²α + cos²α = 1

∴ sin²α + ( )² = 1

∴ sin²α +  = 1

- Subtract    from both sides

∴ sin²α =  

- Take √ for both sides

∴ sin α =  

∵ tan α = sin α ÷ cos α

∴ tan α = ÷

∴ tan α =  

∵ sin β = and 0° < β < 90°

∵ sin²β + cos²β = 1

∴ ( )² + cos²β = 1

∴ + cos²β = 1

- Subtract    from both sides

∴ cos²β =  

- Take √ for both sides

∴ cos β =  

∵ tan β = sin β ÷ cos β

∴ tan β = ÷

∴ tan β =  

- Substitute the values of tan α and tan β in the tan (α + β)

∵ tan(α + β) =

∴ tan(α + β) =

∴ tan(α + β) =

8.

∵ sin(α - β) = sin α cos β - cos α sin β

∴ sin(π - Ф) = sin π cos Ф - cos π sin Ф

∵ sin π = 0 and cos π = -1

∴ sin(π - Ф) = (0) × cos Ф - (-1) × sin Ф

∴ sin(π - Ф) = 0 + sin Ф

∴ sin(π - Ф) = sin Ф

9.

∵ cos 2Ф = 2 cos²Ф - 1

∵ cos Ф =

∴ cos 2Ф = 2 ( )² - 1

∴ cos 2Ф = 2 × - 1

∴ cos 2Ф = - 1

∴ cos 2Ф =

10.

∵ sin 2Ф = 2 sinФ cosФ

∵ cosФ = 0.6 and 0° < Ф < 90°

- That means Ф is in the 1st quadrant and all its trigonometry

   ratios are positive

∵ sin²Ф + cos²Ф = 1

∴ sin²Ф + (0.6)² = 1

∴ sin²Ф + 0.36 = 1

- Subtract 0.36 from both sides

∴ sin²Ф = 0.64

- Take √ for both sides

∴ sinФ = 0.8

- Substitute the values of sinФ and cosФ in the rule above

∴ sin 2Ф = 2(0.8)(0.6)

∴ sin 2Ф = 0.96

answer: median

step-by-step explanation:

the median is the middle value when a data set is ordered from least to greatest

answer: idk

step-by-step explanation: