Find the rate of interest when the principal is Rs. 6000, simple interest is Rs. 900 and time is 5 years.
2 answers:
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Remember the divisibility rule for 9. The sum of the digits of the number must be divisible by nine.
Let the digit be
. Then 
has to be divisible by nine. Recalling that 
, we note that 
.
Let the digit be
We can draw a unit circle as:
The sine is the vertical leg (or vertical projection) of the triangle formed by the angle.
The cosine will be the horizontal leg (or horizontal projection) of this same triangle.
The hypotenuse of this triangle will be the radius if the unit circle (r = 1).
a) The sine will be increasing from θ = 0° until it reaches its maximum at 90°.
Then it will be decreasing for angles between 90° and 270°.
Between 270° and 0° it will be increasing again.
b) The cosine has a maximum value for an angle of 0°.
It will decrease until 180°.
Then it will be increasing from angles between 180° and 360°.
c) We can see in the unit circle that the sine is 0 when the angle is one the horizontal axis, like when θ = 0° or θ = 180°.
The cosine will be equal to 0 when the angle is vertical: θ = 90° and θ = 270°.
Answer:
a) Increasing: (0°, 90°) and (270°, 360°)
Decreasing: (90°, 270°)
b) Increasing: (180°, 360°)
Decreasing: (0°,180°).
c) Sin(θ) = 0 for θ = 0° and θ = 180°
Cos(θ) = 0 for θ = 90° and θ = 270°
