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Cot θ = -24/7 and cos θ < 0
"cos θ < 0" means cosine is negative
Remember osmething like "ALL students Take Calculus"?
all is positive in quadrant 1
sine/cosecant is positive only in quadrant 2
tangent/cotangent is positive only in quadrant 3
cosine/secant is positive only in quadrant 4
since cot(angent) is the reciprocal of tangent, tangent must also be negative.
tangent is negative in quadrants II and IV
cosine is negative in quadrants II and III
therefore, θ must lie in quadrant II.
remember the tan θ = y / x. it is the y-coordinate divided by the x-coodinate. the y-coordinate would be the height of this 90 degree triangle that forms. the x-coordinate would be the bottom leg of the 90 degree triangle
then cot θ = x / y. therefore, cot θ = -24 / 7 means x = -24 and y = 7. we draw a triangle with these dimensions.
csc θ = r / y = hypotenuse over opposite (when you view the reference angle labeled as the one to base the hypotenuse/oppoiste on) because it is the reciprocal of sine
the hypotenuse can be found w/ pythagorean theorem
hypotenuse = √[(-24)² + 7²] = 25
therefore,
cot θ = 25/7
"cos θ < 0" means cosine is negative
Remember osmething like "ALL students Take Calculus"?
all is positive in quadrant 1
sine/cosecant is positive only in quadrant 2
tangent/cotangent is positive only in quadrant 3
cosine/secant is positive only in quadrant 4
since cot(angent) is the reciprocal of tangent, tangent must also be negative.
tangent is negative in quadrants II and IV
cosine is negative in quadrants II and III
therefore, θ must lie in quadrant II.
remember the tan θ = y / x. it is the y-coordinate divided by the x-coodinate. the y-coordinate would be the height of this 90 degree triangle that forms. the x-coordinate would be the bottom leg of the 90 degree triangle
then cot θ = x / y. therefore, cot θ = -24 / 7 means x = -24 and y = 7. we draw a triangle with these dimensions.
csc θ = r / y = hypotenuse over opposite (when you view the reference angle labeled as the one to base the hypotenuse/oppoiste on) because it is the reciprocal of sine
the hypotenuse can be found w/ pythagorean theorem
hypotenuse = √[(-24)² + 7²] = 25
therefore,
cot θ = 25/7
It is given in the question that in the lemon squash 2 parts concentrate is added to 5 parts of water. Thus it makes the concentrate to water ratio as 2:5 or . Now, if this ratio is maintained then the amount of water to be added to 90 ml concentrate in a glass can be calculated as:
Where x is the amount of water to be added, in ml (milliliters).
Cross multiplication of the above equation will give us:
Dividing both sides by 2 we will get:
Thus, if we put 90ml of concentrate in a glass, the water that should be added must be 225 ml.