Difference between revisions of "User:Temperal/sandbox"
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− | < | + | ==Problem 1== |
− | + | ||
− | </ | + | Evaluate the following expressions: |
+ | |||
+ | (a) <math>\tan(45^\circ)</math> | ||
+ | |||
+ | (b) <math>\cos\left(\frac {7\pi}{4}\right)</math> | ||
+ | |||
+ | (c) <math>\sin\left(\frac {5\pi}{3}\right)</math> | ||
+ | |||
+ | (d) <math>\csc(135^\circ)</math> | ||
+ | |||
+ | (e) <math>\cot(945^\circ)</math> | ||
+ | |||
+ | (f) <math>\sin(\pi \sin(\pi/6))</math> | ||
+ | |||
+ | (g) <math>\tan(21\pi)</math> | ||
+ | |||
+ | (h) <math>\sec( - 585^\circ)</math> | ||
+ | |||
+ | ==Problem 2== | ||
+ | |||
+ | Using the unit circle, find <math>\sin \left( x + \frac {\pi}{2} \right)</math> and <math>\cos \left( x + \frac {\pi}{2} \right)</math> in terms of <math>\sin x</math> and <math>\cos x</math>. | ||
+ | |||
+ | |||
+ | ==Problem 3== | ||
+ | |||
+ | In triangle <math>ABC</math>, <math>\angle B = 90^\circ</math>, <math>\sin A = 7/9</math>, and <math>BC = 21</math>. What is <math>AB</math>? | ||
+ | |||
+ | ==Problem 4== | ||
+ | |||
+ | What does the graph of <math>\sin 4x</math> look like compared to the graphs of <math>\sin x</math> and <math>\cos x</math>? What about the graph of <math>2\sin \left( 3x + \frac {\pi}{4} \right) - 1</math>? | ||
+ | |||
+ | |||
+ | |||
+ | ==Problem 5== | ||
+ | |||
+ | Find the value of <math>\tan(\pi/12) \cdot \tan(2\pi/12) \cdot \tan(3\pi/12) \cdots \tan(5\pi/12).</math> | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | ==Problem 6== | ||
+ | |||
+ | Suppose that parallelogram <math>ABCD</math> has <math>\angle A = \angle C = 30^\circ</math>, <math>\angle B = \angle D = 150^\circ</math>, and the shorter diagonal <math>BD</math> has length 2. If the height of the parallelogram is <math>a</math>, find the perimeter of <math>ABCD</math> in terms of <math>a</math>. | ||
+ | |||
+ | |||
+ | |||
+ | ==Problem 7== | ||
+ | |||
+ | Given a positive number <math>n</math> and a number <math>c</math> satisfying <math>- 1 < c < 1</math>, for how many values of <math>q</math> with <math>0 \leq q < 2\pi</math> is <math>\sin nq = c</math>? What if <math>c = 1</math> or <math>c = - 1</math>? | ||
+ | |||
+ | |||
+ | |||
+ | ==Problem 8== | ||
+ | |||
+ | How many solutions are there to the equation <math>\cos x = \frac {x^2}{1000}</math>, where <math>x</math> is in radians? | ||
+ | |||
+ | |||
+ | |||
+ | ==Problem 9== | ||
+ | |||
+ | Determine all <math>\theta</math> such that <math>0 \le \theta \le \frac {\pi}{2}</math> and <math>\sin^5\theta + \cos^5\theta = 1</math>. | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | ==Problem 10== | ||
+ | |||
+ | Find the value of <math>\sin(15^\circ)</math>. Hint: Draw an isosceles triangle with vertex angle <math>30^\circ</math>. |
Latest revision as of 13:28, 24 March 2020
Contents
Problem 1
Evaluate the following expressions:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Problem 2
Using the unit circle, find and
in terms of
and
.
Problem 3
In triangle ,
,
, and
. What is
?
Problem 4
What does the graph of look like compared to the graphs of
and
? What about the graph of
?
Problem 5
Find the value of
Problem 6
Suppose that parallelogram has
,
, and the shorter diagonal
has length 2. If the height of the parallelogram is
, find the perimeter of
in terms of
.
Problem 7
Given a positive number and a number
satisfying
, for how many values of
with
is
? What if
or
?
Problem 8
How many solutions are there to the equation , where
is in radians?
Problem 9
Determine all such that
and
.
Problem 10
Find the value of . Hint: Draw an isosceles triangle with vertex angle
.