Arithmetic Sequences
Arithmetic Series
Cofunction Identities
Double Argument Properties
Pythagorean Identities
100
The formula for an arithmetic sequence.
What is An = A1 + (n-1)d
100
Write the formula for the partial sum of an arithmetic series.
What is Sn = n ((A1 + An) / 2).
100
Express \[\sin \left( {\frac{\pi }{2} - x} \right)\] as the trig function of a single argument.
\[\cos x\]
100
Express \[\cos (A - B)\] using only single argument(s) A and/or B.
\[\cos A\cos B + \sin A\sin B\]
100
Express \[1 - {\cos ^2}x\] in terms of one trig function.
\[{\sin ^2}x\]
200
Find the 20th term of the arithmetic sequence 9, 16, 23, 30,..... using the formula.
What is 142.
200
Find the sum of 2 + 4 + 6 + .... + 100.
What is 2550.
200
Express \[\cot x\]using its co-function.
\[\tan \left( {\frac{\pi }{2} - x} \right)\]
200
Express \[\sin (A + B)\] using only single argument(s) A and/or B.
\[\sin A\cos B + \cos A\sin B\]
200
Give a Pythagorean Trig Property that contains secant.
\[{\tan ^2} + 1 = {\sec ^2}x\]
300
Write an equation for the nth term of the sequence where A1 = 12 and d=8.
What is An = 8n + 4.
300
Find the first three terms of the arithmetic series in which A1 = 48, An = 180, and Sn = 1368.
What is 48, 60, 72.
300
\[Arc\cos \left[ {\sin \left( {{{34}^ \circ }} \right)} \right]\]
\[{56^ \circ }\]
300
Express \[\tan (A - B)\] using only the tangent function of single argument(s) A and/or B.
\[\frac{{\tan A - \tan B}}{{1 + \tan A\tan B}}\]
300
Evaluate: \[{\csc ^2}x - {\cot ^2}x\]
1
400
Find the arithmetic means in the sequence 21, ___, ___, ___, 45,......
What is 27, 33, 39.
400
Find the first three terms of the arithmetic series in which Sn = 120, n = 8, and An = 36.
What is -6, 0, 6.
400
\[Arc\cot \left[ {\tan \left( {\frac{\pi }{6}} \right)} \right]\]
\[\frac{\pi }{3}\]
400
Find the exact value of \[\sin ({75^ \circ })\]
\[\frac{{\sqrt 2 + \sqrt 6 }}{4}\]
400
Evaluate: \[{\tan ^2}x - {\sec ^2}x\]
-1
500
Joe averaged 123 total pins per game in his bowling league this season. He is taking bowling lessons and hopes to bring his average up by 8 pins each new season. Write an equation to represent the nth term of the sequence.
What is An = 8n + 115.
500
A construction company will be fined for each day it is late completing its current project. The daily fine will be $4000 for the first day and will increase by $1000 each day. Based on its budget, the company can only afford $60000 in total fines. What is the maximum number of days it can be late?
8 days
500
\[Arc\sec \left[ {\csc \left( {{{17.9}^ \circ }} \right)} \right]\]
\[{72.1^ \circ }\]
500
Find the exact value of \[\cos \left( {{{105}^ \circ }^{}} \right)\]
\[ - \frac{{\sqrt 6 - \sqrt 2 }}{4}\]
500
Express \[{\tan ^2}x - {\sec ^2}x + {\sin ^2}x\] using only one trigonometric function.
\[ - {\cos ^2}x\]
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