Trigonometry Solutions
30 trigonometry problems covering identities, graph/property analysis, and triangle-solving patterns — with reference solutions and marking schemes.
30 problems
Problem 1: find
Tangent Sum Formula Application Given that and , find .
Problem 2: Cosine Sum Formula Evaluate
Cosine Sum Formula Evaluate .
Problem 3: find
Roots and Tangent Formula Given that and are roots of , find .
Problem 4: find
Sine Sum Formula Application Given and , find .
Problem 5: find
Sum of Squares Method Given and , find .
Problem 6: find
Double-Angle Formula Given and , find .
Problem 7: find
Reduction and Double-Angle Given , find .
Problem 8: Angle Evaluation Evaluate
Angle Evaluation Evaluate .
Problem 9: find
Auxiliary Angle Method Given , find .
Problem 10: find
Value Finding Comprehensive Given , find .
Problem 11: Find the domain of
Domain of Trigonometric Function Find the domain of .
Problem 12: find
Even Function Parameter Given where is an even function, find .
Problem 13: find
Graph Translation and Symmetry Translate left by units ( ). If the resulting graph is symmetric about the y-axis, find .
Problem 14: Find the minimum positive period of
Period of Product Function Find the minimum positive period of .
Problem 15: Find the minimum positive period of
Period of Tangent Composition Find the minimum positive period of .
Problem 16: Find the range of for
Range of Trigonometric Function Find the range of for .
Problem 17: find the range of
Range and Domain Relationship Given with domain ( ) and range , find the range of .
Problem 18: find the minimum value of
Zero Points Problem Given ( ). If and has exactly one zero in , find the minimum value of .
Problem 19: find the range of
Monotonicity Interval Given ( ). If is monotonically increasing on , find the range of .
Problem 20: Find
Maximum Value Problem Given ( ) has its graph symmetric about , and has no minimum value on . Find .
Problem 21: find
Law of Sines Basic Application In , given , , and , find .
Problem 22: find angle
Law of Sines Side-Angle Conversion In , let sides opposite to angles be . Given and , find angle .
Problem 23: find the circumradius of
Circumradius from Law of Cosines In , given , , and , find the circumradius of .
Problem 24: Determine the type of triangle
Triangle Shape Determination In , given and . Determine the type of triangle.
Problem 25: Find the area of
Triangle Area Formula In , given , , and . Find the area of .
Problem 26: Find the maximum perimeter of
Maximum Perimeter Problem In , given and . Find the maximum perimeter of .
Problem 27: Find the maximum area of
Maximum Area Problem In , given and . Find the maximum area of .
Problem 28: Find the maximum area of quadrilateral
Quadrilateral Area Maximum In convex quadrilateral , , , , , and . Find the maximum area of quadrilateral .
Problem 29: Find
Comprehensive Application In , given and . (1) Find . (2) If , find the area of .
Problem 30: determine the shape of the triangle
Equilateral Triangle Verification In , sides are in arithmetic progression. The circle with diameter has area . If the area of is , determine the shape of the t