A chemist needs 30mL of a 12% acid solution for an experiment. The lab has available a 10% solution and a 25% solution. How many
1 answer:
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Answer:
Step-by-step explanation:
Start by noticing that the angle is on the 4th quadrant (between
and
. Recall then that in this quadrant the functions tangent and cosine are positive, while the function sine is negative in value. This is important to remember given the fact that tangent of an angle is defined as the quotient of the sine function at that angle divided by the cosine of the same angle:
Now, let's use the information that the tangent of the angle in question equals "-1", and understand what that angle could be:
The particular special angle that satisfies this (the magnitude of sine and cosine the same) in the 4th quadrant, is the angle
which renders for the cosine function the value .
Now, since we are asked to find the value of the secant of this angle, we need to remember the expression for the secant function in terms of other trig functions:
Therefore the value of the secant of this angle would be the reciprocal of the cosine of the angle, that is:
Answer:
Step-by-step explanation:
We are looking for a trigonometric function which contains the point (0, 3), and has an amplitude of 3.
We know that for a sine function ,
; therefore the function we a looking for cannot be a sine function because it is zero at
.
However, the cosine function gives non-zero value at
therefore, a cosine function can be our function.
Now, cosine function with amplitude has the form
this is because the cosine function is maximum at and therefore, has the property that
in other words it contains the point .
The function we are looking for contains the point ; therefore, its amplitude must be 3, or
we see that this function satisfies our conditions: has amplitude of 3, and it passes through the point (0, 3) because