Answer:
The solutions of the equation are -41.8° , 0.0° , 41.8°
Step-by-step explanation:
∵ 3 sin²Ф - 2 sinФ = 0 is a quadratic function
∵ The domain of the function is -90° ≤ Ф ≤ 90°
- Lets take sinФ as a common factor
∴ sinФ (3 sinФ - 2) = 0
- Two terms multiplied by each other = 0
∴ One of them must be equal zero
∴ sinФ = 0 or 3 sinФ - 2 = 0
- If sinФ = 0 ⇒ Ф = 0.0°
- If 3 sinФ - 2 = 0 ⇒ 3 sinФ = 2 ⇒ sin Ф = 2/3
∵ sinФ 2/3
∴ Ф = 41.8° ⇒ Ф ≤ 90° (in first quadrant)
∵ -90° ≤ Ф ≤ 90°
∴ Ф = -41.8° ⇒ Ф ≥ -90° (in fourth quadrant)
∴ The solutions of the equation are -41.8° , 0.0° , 41.8°
The top graph
hope this help
Answer:

Step-by-step explanation:
In the given figure, PQRS is a rhombus and SRM is an equilateral triangle.
We are also given that SN⊥RM and that ∠PRS = 55°.
And we want to find the measure of ∠QSN.
Remember that since PQRS is a rhombus, the angles formed by its diagonals are right angles. Let the intersection point of the diagonals be K. Therefore:

Now, RKS is also a triangle. The interior angles of all triangles must be 180. Thus:

Substitute in known values:

Solve for ∠KSR:

Since SRM is an equilateral triangle, this means that:

Note that RNS is also a triangle. Therefore:

Substitute in known values:

So:

∠QSN is the addition of the two angles:

Therefore:
